# Syllabus to learn statistics ## PHASE 0 - FOUNDATIONAL MATHEMATICS ### Day 1: Functions: concept and notation - Foundations * **Objective:** Build a solid conceptual understanding of *functions: concept and notation*. * **Theory:** A function maps every input to exactly one output; domain and range define what is allowed in and out. * **Practice:** Summarize the concept in your own words and give one real-world example before moving to application. ### Day 2: Functions: concept and notation - Applied Practice * **Objective:** Apply *functions: concept and notation* to solve concrete problems and solidify intuition. * **Theory (recap):** A function maps every input to exactly one output; domain and range define what is allowed in and out. * **Practice:** Write 3 examples of functions you use daily (e.g. price -> tax) and identify domain/range. ### Day 3: Logarithms - Foundations * **Objective:** Build a solid conceptual understanding of *logarithms*. * **Theory:** Logarithms are the inverse of exponentiation; they compress large ranges and turn multiplication into addition. log rules: log(ab)=log a + log b, log(a/b)=log a - log b, log(a^n)=n log a. * **Practice:** Summarize the concept in your own words and give one real-world example before moving to application. ### Day 4: Logarithms - Applied Practice * **Objective:** Apply *logarithms* to solve concrete problems and solidify intuition. * **Theory (recap):** Logarithms are the inverse of exponentiation; they compress large ranges and turn multiplication into addition. * **Practice:** Solve 10 log equations and explain why log-scale is used for skewed data like income. ### Day 5: Exponential functions - Foundations * **Objective:** Build a solid conceptual understanding of *exponential functions*. * **Theory:** Exponential growth/decay: y = a \* e^(kx); the rate of change is proportional to the current value. Connection to compound interest and to the exponential distribution. * **Practice:** Summarize the concept in your own words and give one real-world example before moving to application. ### Day 6: Exponential functions - Applied Practice * **Objective:** Apply *exponential functions* to solve concrete problems and solidify intuition. * **Theory (recap):** Exponential growth/decay: y = a \* e^(kx); the rate of change is proportional to the current value. * **Practice:** Plot exponential growth vs decay curves and identify the half-life/doubling time. ### Day 7: Sigma notation (summation) - Foundations * **Objective:** Build a solid conceptual understanding of *sigma notation (summation)*. * **Theory:** Sigma notation compactly represents repeated addition, e.g. sum of x\_i from i=1 to n. * **Practice:** Summarize the concept in your own words and give one real-world example before moving to application. ### Day 8: Sigma notation (summation) - Applied Practice * **Objective:** Apply *sigma notation (summation)* to solve concrete problems and solidify intuition. * **Theory (recap):** Sigma notation compactly represents repeated addition, e.g. sum of x\_i from i=1 to n. * **Practice:** Rewrite 5 formulas (mean, variance) fully in sigma notation from scratch. ### Day 9: Vectors: definition and operations - Introduction * **Objective:** Grasp the core intuition behind *vectors: definition and operations* before the mechanics. * **Theory:** A vector is an ordered list of numbers representing magnitude and direction; supports addition, scalar multiplication. * **Practice:** Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences. ### Day 10: Vectors: definition and operations - Deep Dive * **Objective:** Understand the full mechanics/derivation behind *vectors: definition and operations*. * **Theory:** A vector is an ordered list of numbers representing magnitude and direction; supports addition, scalar multiplication. Vector norm (length) and the dot product measure size and alignment between vectors. * **Practice:** Derive or re-derive the key formula/result by hand, step by step. ### Day 11: Vectors: definition and operations - Applied Practice * **Objective:** Apply *vectors: definition and operations* to a concrete problem or dataset. * **Theory (recap):** Vector norm (length) and the dot product measure size and alignment between vectors. * **Practice:** Compute the norm and dot product of 5 vector pairs by hand, then verify with NumPy. ### Day 12: Matrices: definition and notation - Foundations * **Objective:** Build a solid conceptual understanding of *matrices: definition and notation*. * **Theory:** A matrix is a rectangular array of numbers; rows/columns encode structured data (e.g. a dataset). * **Practice:** Summarize the concept in your own words and give one real-world example before moving to application. ### Day 13: Matrices: definition and notation - Applied Practice * **Objective:** Apply *matrices: definition and notation* to solve concrete problems and solidify intuition. * **Theory (recap):** A matrix is a rectangular array of numbers; rows/columns encode structured data (e.g. a dataset). * **Practice:** Represent a small dataset (5 rows, 3 features) as a matrix and label its dimensions. ### Day 14: Matrix operations - Foundations * **Objective:** Build a solid conceptual understanding of *matrix operations*. * **Theory:** Matrix addition and multiplication follow strict dimension rules; multiplication is not commutative. The identity matrix and matrix inverse play the role of '1' and division in matrix algebra. * **Practice:** Summarize the concept in your own words and give one real-world example before moving to application. ### Day 15: Matrix operations - Applied Practice * **Objective:** Apply *matrix operations* to solve concrete problems and solidify intuition. * **Theory (recap):** Matrix addition and multiplication follow strict dimension rules; multiplication is not commutative. * **Practice:** Multiply 3 matrix pairs by hand, then verify using NumPy; try one non-conformable pair and explain the error. ### Day 16: Solving systems of linear equations - Foundations * **Objective:** Build a solid conceptual understanding of *solving systems of linear equations*. * **Theory:** A system of linear equations can be written as Ax = b and solved via elimination or matrix inversion. Systems can be consistent (unique/infinite solutions) or inconsistent (no solution). * **Practice:** Summarize the concept in your own words and give one real-world example before moving to application. ### Day 17: Solving systems of linear equations - Applied Practice * **Objective:** Apply *solving systems of linear equations* to solve concrete problems and solidify intuition. * **Theory (recap):** A system of linear equations can be written as Ax = b and solved via elimination or matrix inversion. * **Practice:** Solve 5 systems of equations by hand, then confirm each with numpy.linalg.solve. ### Day 18: Eigenvalues and eigenvectors (intuition) - Introduction * **Objective:** Grasp the core intuition behind *eigenvalues and eigenvectors (intuition)* before the mechanics. * **Theory:** An eigenvector of a matrix points in a direction that the matrix only stretches, not rotates; the eigenvalue is the stretch factor. * **Practice:** Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences. ### Day 19: Eigenvalues and eigenvectors (intuition) - Deep Dive * **Objective:** Understand the full mechanics/derivation behind *eigenvalues and eigenvectors (intuition)*. * **Theory:** An eigenvector of a matrix points in a direction that the matrix only stretches, not rotates; the eigenvalue is the stretch factor. Eigen-decomposition underlies PCA, covariance structure, and stability analysis. * **Practice:** Derive or re-derive the key formula/result by hand, step by step. ### Day 20: Eigenvalues and eigenvectors (intuition) - Applied Practice * **Objective:** Apply *eigenvalues and eigenvectors (intuition)* to a concrete problem or dataset. * **Theory (recap):** Eigen-decomposition underlies PCA, covariance structure, and stability analysis. * **Practice:** Compute eigenvalues/eigenvectors of a 2x2 matrix by hand and visualize the transformation. ### Day 21: Derivatives - Introduction * **Objective:** Grasp the core intuition behind *derivatives* before the mechanics. * **Theory:** A derivative measures the instantaneous rate of change of a function; it is the slope of the tangent line. * **Practice:** Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences. ### Day 22: Derivatives - Deep Dive * **Objective:** Understand the full mechanics/derivation behind *derivatives*. * **Theory:** A derivative measures the instantaneous rate of change of a function; it is the slope of the tangent line. Common rules: power rule, product rule, chain rule. * **Practice:** Derive or re-derive the key formula/result by hand, step by step. ### Day 23: Derivatives - Applied Practice * **Objective:** Apply *derivatives* to a concrete problem or dataset. * **Theory (recap):** Common rules: power rule, product rule, chain rule. * **Practice:** Differentiate 10 functions by hand and verify symbolically with SymPy. ### Day 24: Partial derivatives - Foundations * **Objective:** Build a solid conceptual understanding of *partial derivatives*. * **Theory:** A partial derivative measures how a multivariable function changes with respect to one variable, holding others fixed. Partial derivatives are the building block of gradients used in optimization (e.g. least squares, gradient descent). * **Practice:** Summarize the concept in your own words and give one real-world example before moving to application. ### Day 25: Partial derivatives - Applied Practice * **Objective:** Apply *partial derivatives* to solve concrete problems and solidify intuition. * **Theory (recap):** A partial derivative measures how a multivariable function changes with respect to one variable, holding others fixed. * **Practice:** Compute partial derivatives of a 2-variable loss function and find its minimum by hand. ### Day 26: Integrals - Foundations * **Objective:** Build a solid conceptual understanding of *integrals*. * **Theory:** An integral accumulates area under a curve; it is the inverse operation of differentiation. Definite integrals compute exact accumulated quantities (e.g. probability over an interval). * **Practice:** Summarize the concept in your own words and give one real-world example before moving to application. ### Day 27: Integrals - Applied Practice * **Objective:** Apply *integrals* to solve concrete problems and solidify intuition. * **Theory (recap):** An integral accumulates area under a curve; it is the inverse operation of differentiation. * **Practice:** Compute 5 definite integrals by hand and confirm with SciPy's quad. ### Day 28: Why a PDF must integrate to 1 - Introduction * **Objective:** Grasp the core intuition behind *why a pdf must integrate to 1* before the mechanics. * **Theory:** A probability density function describes relative likelihood; total probability across all outcomes must equal 1 by the axioms of probability. * **Practice:** Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences. ### Day 29: Why a PDF must integrate to 1 - Deep Dive * **Objective:** Understand the full mechanics/derivation behind *why a pdf must integrate to 1*. * **Theory:** A probability density function describes relative likelihood; total probability across all outcomes must equal 1 by the axioms of probability. This constraint is what lets us normalize arbitrary non-negative functions into valid densities. * **Practice:** Derive or re-derive the key formula/result by hand, step by step. ### Day 30: Why a PDF must integrate to 1 - Applied Practice * **Objective:** Apply *why a pdf must integrate to 1* to a concrete problem or dataset. * **Theory (recap):** This constraint is what lets us normalize arbitrary non-negative functions into valid densities. * **Practice:** Verify by integration that the Normal and Exponential PDFs each integrate to 1 over their support. ### Day 31: Multivariable calculus basics - Foundations * **Objective:** Build a solid conceptual understanding of *multivariable calculus basics*. * **Theory:** Gradients generalize the derivative to multiple dimensions and point in the direction of steepest increase. Multivariable calculus underlies optimization of loss functions with many parameters. * **Practice:** Summarize the concept in your own words and give one real-world example before moving to application. ### Day 32: Multivariable calculus basics - Applied Practice * **Objective:** Apply *multivariable calculus basics* to solve concrete problems and solidify intuition. * **Theory (recap):** Gradients generalize the derivative to multiple dimensions and point in the direction of steepest increase. * **Practice:** Compute the gradient of a simple 2-parameter loss function and interpret its direction. ### Day 33: Why expectation is an integral - Foundations * **Objective:** Build a solid conceptual understanding of *why expectation is an integral*. * **Theory:** Expectation is a probability-weighted average; for continuous variables this weighted sum becomes an integral of x \* f(x). This connects calculus directly to the core statistical concept of the mean of a random variable. * **Practice:** Summarize the concept in your own words and give one real-world example before moving to application. ### Day 34: Why expectation is an integral - Applied Practice * **Objective:** Apply *why expectation is an integral* to solve concrete problems and solidify intuition. * **Theory (recap):** Expectation is a probability-weighted average; for continuous variables this weighted sum becomes an integral of x \* f(x). * **Practice:** Derive E\[X\] for the Uniform(0,1) distribution by hand using integration. ### Day 35: Vector spaces - Introduction * **Objective:** Grasp the core intuition behind *vector spaces* before the mechanics. * **Theory:** A vector space is a set of vectors closed under addition and scalar multiplication, satisfying specific axioms. * **Practice:** Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences. ### Day 36: Vector spaces - Deep Dive * **Objective:** Understand the full mechanics/derivation behind *vector spaces*. * **Theory:** A vector space is a set of vectors closed under addition and scalar multiplication, satisfying specific axioms. Statistical models live inside vector spaces (e.g. the space of possible regression coefficients). * **Practice:** Derive or re-derive the key formula/result by hand, step by step. ### Day 37: Vector spaces - Applied Practice * **Objective:** Apply *vector spaces* to a concrete problem or dataset. * **Theory (recap):** Statistical models live inside vector spaces (e.g. the space of possible regression coefficients). * **Practice:** Check whether 3 given sets qualify as vector spaces by testing the axioms. ### Day 38: Basis and dimension - Foundations * **Objective:** Build a solid conceptual understanding of *basis and dimension*. * **Theory:** A basis is a minimal set of vectors that spans a vector space; dimension is the number of vectors needed. Choosing a good basis (e.g. principal components) simplifies high-dimensional data. * **Practice:** Summarize the concept in your own words and give one real-world example before moving to application. ### Day 39: Basis and dimension - Applied Practice * **Objective:** Apply *basis and dimension* to solve concrete problems and solidify intuition. * **Theory (recap):** A basis is a minimal set of vectors that spans a vector space; dimension is the number of vectors needed. * **Practice:** Find a basis for a given 2D and 3D subspace and confirm linear independence. ### Day 40: Orthogonality - Foundations * **Objective:** Build a solid conceptual understanding of *orthogonality*. * **Theory:** Orthogonal vectors have a zero dot product and represent independent directions. Orthogonality underlies uncorrelated predictors in regression and independent components in PCA. * **Practice:** Summarize the concept in your own words and give one real-world example before moving to application. ### Day 41: Orthogonality - Applied Practice * **Objective:** Apply *orthogonality* to solve concrete problems and solidify intuition. * **Theory (recap):** Orthogonal vectors have a zero dot product and represent independent directions. * **Practice:** Check orthogonality of vector pairs and orthogonalize a non-orthogonal pair via Gram-Schmidt. ### Day 42: Projections - Introduction * **Objective:** Grasp the core intuition behind *projections* before the mechanics. * **Theory:** Projecting a vector onto another finds the closest point in that direction; this is the geometric basis of least-squares regression. * **Practice:** Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences. ### Day 43: Projections - Deep Dive * **Objective:** Understand the full mechanics/derivation behind *projections*. * **Theory:** Projecting a vector onto another finds the closest point in that direction; this is the geometric basis of least-squares regression. The residual in regression is exactly the part of y orthogonal to the projection onto predictor space. * **Practice:** Derive or re-derive the key formula/result by hand, step by step. ### Day 44: Projections - Applied Practice * **Objective:** Apply *projections* to a concrete problem or dataset. * **Theory (recap):** The residual in regression is exactly the part of y orthogonal to the projection onto predictor space. * **Practice:** Project a vector onto another by hand and relate the result to fitting a simple regression line. ### Day 45: Linear algebra foundations for Regression - Foundations * **Objective:** Build a solid conceptual understanding of *linear algebra foundations for regression*. * **Theory:** Regression coefficients solve a projection problem: finding the linear combination of predictors closest to y. * **Practice:** Summarize the concept in your own words and give one real-world example before moving to application. ### Day 46: Linear algebra foundations for Regression - Applied Practice * **Objective:** Apply *linear algebra foundations for regression* to solve concrete problems and solidify intuition. * **Theory (recap):** Regression coefficients solve a projection problem: finding the linear combination of predictors closest to y. * **Practice:** Derive the normal equations (X^T X)b = X^T y from the projection viewpoint. ### Day 47: Linear algebra foundations for PCA - Foundations * **Objective:** Build a solid conceptual understanding of *linear algebra foundations for pca*. * **Theory:** PCA finds the eigenvectors of the covariance matrix, i.e. the orthogonal directions of maximum variance. * **Practice:** Summarize the concept in your own words and give one real-world example before moving to application. ### Day 48: Linear algebra foundations for PCA - Applied Practice * **Objective:** Apply *linear algebra foundations for pca* to solve concrete problems and solidify intuition. * **Theory (recap):** PCA finds the eigenvectors of the covariance matrix, i.e. the orthogonal directions of maximum variance. * **Practice:** Explain in your own words why PCA is an eigenvalue problem on the covariance matrix. ### Day 49: Linear algebra foundations for Factor Analysis - Foundations * **Objective:** Build a solid conceptual understanding of *linear algebra foundations for factor analysis*. * **Theory:** Factor Analysis models observed variables as linear combinations of fewer latent (unobserved) factors plus noise. * **Practice:** Summarize the concept in your own words and give one real-world example before moving to application. ### Day 50: Linear algebra foundations for Factor Analysis - Applied Practice * **Objective:** Apply *linear algebra foundations for factor analysis* to solve concrete problems and solidify intuition. * **Theory (recap):** Factor Analysis models observed variables as linear combinations of fewer latent (unobserved) factors plus noise. * **Practice:** Compare PCA and Factor Analysis conceptually: variance explained vs latent causal structure. ### Day 51: Linear algebra foundations for Machine Learning - Foundations * **Objective:** Build a solid conceptual understanding of *linear algebra foundations for machine learning*. * **Theory:** Most ML models (linear/logistic regression, neural nets, SVMs) are fundamentally matrix and vector operations. * **Practice:** Summarize the concept in your own words and give one real-world example before moving to application. ### Day 52: Linear algebra foundations for Machine Learning - Applied Practice * **Objective:** Apply *linear algebra foundations for machine learning* to solve concrete problems and solidify intuition. * **Theory (recap):** Most ML models (linear/logistic regression, neural nets, SVMs) are fundamentally matrix and vector operations. * **Practice:** Trace how a simple neural network layer (Wx + b) is pure linear algebra. ### Day 53: Review: Foundational math recap * **Objective:** Understand and internalize *review: foundational math recap*. * **Theory:** Consolidate algebra, calculus, and linear algebra concepts learned so far before moving into probability. * **Practice:** Take a 20-question mixed review quiz covering functions, derivatives, integrals, vectors, and matrices. ### Day 54: Practice: comprehensive math foundations problem set * **Objective:** Understand and internalize *practice: comprehensive math foundations problem set*. * **Theory:** Apply all foundational math tools together on realistic mini-problems. * **Practice:** Complete a problem set that combines calculus and linear algebra (e.g. derive least squares by hand). ## PHASE 1 - DESCRIPTIVE STATISTICS ### Day 55: Arithmetic mean - Foundations * **Objective:** Build a solid conceptual understanding of *arithmetic mean*. * **Theory:** The arithmetic mean sums all values and divides by the count; it represents the 'balance point' of the data. * **Practice:** Summarize the concept in your own words and give one real-world example before moving to application. ### Day 56: Arithmetic mean - Applied Practice * **Objective:** Apply *arithmetic mean* to solve concrete problems and solidify intuition. * **Theory (recap):** The arithmetic mean sums all values and divides by the count; it represents the 'balance point' of the data. * **Practice:** Compute the mean of a small dataset by hand and verify with Python. ### Day 57: Weighted mean - Foundations * **Objective:** Build a solid conceptual understanding of *weighted mean*. * **Theory:** A weighted mean gives different importance to each observation, useful when data points are not equally reliable. * **Practice:** Summarize the concept in your own words and give one real-world example before moving to application. ### Day 58: Weighted mean - Applied Practice * **Objective:** Apply *weighted mean* to solve concrete problems and solidify intuition. * **Theory (recap):** A weighted mean gives different importance to each observation, useful when data points are not equally reliable. * **Practice:** Compute a GPA (weighted by credit hours) using the weighted mean formula. ### Day 59: Geometric mean - Foundations * **Objective:** Build a solid conceptual understanding of *geometric mean*. * **Theory:** The geometric mean is the nth root of the product of n values; it is appropriate for multiplicative processes like growth rates. * **Practice:** Summarize the concept in your own words and give one real-world example before moving to application. ### Day 60: Geometric mean - Applied Practice * **Objective:** Apply *geometric mean* to solve concrete problems and solidify intuition. * **Theory (recap):** The geometric mean is the nth root of the product of n values; it is appropriate for multiplicative processes like growth rates. * **Practice:** Compute the geometric mean of 5 years of investment returns and compare it to the arithmetic mean. ### Day 61: Harmonic mean - Introduction * **Objective:** Grasp the core intuition behind *harmonic mean* before the mechanics. * **Theory:** The harmonic mean is the reciprocal of the average of reciprocals; it suits rates like speed or price-per-unit. * **Practice:** Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences. ### Day 62: Harmonic mean - Deep Dive * **Objective:** Understand the full mechanics/derivation behind *harmonic mean*. * **Theory:** The harmonic mean is the reciprocal of the average of reciprocals; it suits rates like speed or price-per-unit. * **Practice:** Derive or re-derive the key formula/result by hand, step by step. ### Day 63: Harmonic mean - Applied Practice * **Objective:** Apply *harmonic mean* to a concrete problem or dataset. * **Theory (recap):** The harmonic mean is the reciprocal of the average of reciprocals; it suits rates like speed or price-per-unit. * **Practice:** Compute the harmonic mean of speeds for a trip with equal distances at different speeds. ### Day 64: Why mean is sensitive to outliers - Foundations * **Objective:** Build a solid conceptual understanding of *why mean is sensitive to outliers*. * **Theory:** A single extreme value can shift the arithmetic mean drastically because every value contributes proportionally to the sum. * **Practice:** Summarize the concept in your own words and give one real-world example before moving to application. ### Day 65: Why mean is sensitive to outliers - Applied Practice * **Objective:** Apply *why mean is sensitive to outliers* to solve concrete problems and solidify intuition. * **Theory (recap):** A single extreme value can shift the arithmetic mean drastically because every value contributes proportionally to the sum. * **Practice:** Add one extreme outlier to a dataset and observe how much the mean shifts vs the median. ### Day 66: Median - Foundations * **Objective:** Build a solid conceptual understanding of *median*. * **Theory:** The median is the middle value of sorted data; it is robust to outliers because it depends only on rank, not magnitude. * **Practice:** Summarize the concept in your own words and give one real-world example before moving to application. ### Day 67: Median - Applied Practice * **Objective:** Apply *median* to solve concrete problems and solidify intuition. * **Theory (recap):** The median is the middle value of sorted data; it is robust to outliers because it depends only on rank, not magnitude. * **Practice:** Compute the median of 3 datasets, one with a heavy outlier, and compare stability to the mean. ### Day 68: Quantiles and percentiles - Foundations * **Objective:** Build a solid conceptual understanding of *quantiles and percentiles*. * **Theory:** Quantiles divide sorted data into equal-sized groups; percentiles are quantiles expressed out of 100. Common quantiles: quartiles (4 groups), deciles (10 groups). * **Practice:** Summarize the concept in your own words and give one real-world example before moving to application. ### Day 69: Quantiles and percentiles - Applied Practice * **Objective:** Apply *quantiles and percentiles* to solve concrete problems and solidify intuition. * **Theory (recap):** Quantiles divide sorted data into equal-sized groups; percentiles are quantiles expressed out of 100. * **Practice:** Compute the 25th, 50th, and 75th percentiles of a dataset by hand and with numpy.percentile. ### Day 70: Interquartile range (IQR) - Foundations * **Objective:** Build a solid conceptual understanding of *interquartile range (iqr)*. * **Theory:** IQR = Q3 - Q1 measures the spread of the middle 50% of data and is robust to outliers. IQR is used to define outlier thresholds (below Q1-1.5*IQR or above Q3+1.5*IQR). * **Practice:** Summarize the concept in your own words and give one real-world example before moving to application. ### Day 71: Interquartile range (IQR) - Applied Practice * **Objective:** Apply *interquartile range (iqr)* to solve concrete problems and solidify intuition. * **Theory (recap):** IQR = Q3 - Q1 measures the spread of the middle 50% of data and is robust to outliers. * **Practice:** Compute IQR for a dataset and flag any outliers using the 1.5\*IQR rule. ### Day 72: Median vs Mean: when to use each - Foundations * **Objective:** Build a solid conceptual understanding of *median vs mean: when to use each*. * **Theory:** Use the median for skewed data or data with outliers (e.g. income); use the mean for symmetric, well-behaved data. * **Practice:** Summarize the concept in your own words and give one real-world example before moving to application. ### Day 73: Median vs Mean: when to use each - Applied Practice * **Objective:** Apply *median vs mean: when to use each* to solve concrete problems and solidify intuition. * **Theory (recap):** Use the median for skewed data or data with outliers (e.g. income); use the mean for symmetric, well-behaved data. * **Practice:** Given 3 real-world datasets, decide and justify whether mean or median better represents each. ### Day 74: Variance - Introduction * **Objective:** Grasp the core intuition behind *variance* before the mechanics. * **Theory:** Variance measures the average squared deviation from the mean, capturing how spread out the data is. * **Practice:** Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences. ### Day 75: Variance - Deep Dive * **Objective:** Understand the full mechanics/derivation behind *variance*. * **Theory:** Variance measures the average squared deviation from the mean, capturing how spread out the data is. Population variance divides by n; sample variance divides by n-1 (Bessel's correction). * **Practice:** Derive or re-derive the key formula/result by hand, step by step. ### Day 76: Variance - Applied Practice * **Objective:** Apply *variance* to a concrete problem or dataset. * **Theory (recap):** Population variance divides by n; sample variance divides by n-1 (Bessel's correction). * **Practice:** Compute variance by hand for a small dataset, then explain why n-1 is used for sample variance. ### Day 77: Standard deviation - Foundations * **Objective:** Build a solid conceptual understanding of *standard deviation*. * **Theory:** Standard deviation is the square root of variance, expressed in the same units as the original data. It quantifies typical distance of observations from the mean. * **Practice:** Summarize the concept in your own words and give one real-world example before moving to application. ### Day 78: Standard deviation - Applied Practice * **Objective:** Apply *standard deviation* to solve concrete problems and solidify intuition. * **Theory (recap):** Standard deviation is the square root of variance, expressed in the same units as the original data. * **Practice:** Compute the standard deviation of 3 datasets and interpret what it means in context (e.g. exam scores). ### Day 79: Coefficient of variation - Foundations * **Objective:** Build a solid conceptual understanding of *coefficient of variation*. * **Theory:** The coefficient of variation (SD/mean) allows comparing variability across datasets with different units or scales. * **Practice:** Summarize the concept in your own words and give one real-world example before moving to application. ### Day 80: Coefficient of variation - Applied Practice * **Objective:** Apply *coefficient of variation* to solve concrete problems and solidify intuition. * **Theory (recap):** The coefficient of variation (SD/mean) allows comparing variability across datasets with different units or scales. * **Practice:** Compare the variability of two datasets with different units using the coefficient of variation. ### Day 81: Spread, dispersion, and volatility - Foundations * **Objective:** Build a solid conceptual understanding of *spread, dispersion, and volatility*. * **Theory:** These terms all describe how scattered data is around a central value, used interchangeably across stats, finance, and engineering. * **Practice:** Summarize the concept in your own words and give one real-world example before moving to application. ### Day 82: Spread, dispersion, and volatility - Applied Practice * **Objective:** Apply *spread, dispersion, and volatility* to solve concrete problems and solidify intuition. * **Theory (recap):** These terms all describe how scattered data is around a central value, used interchangeably across stats, finance, and engineering. * **Practice:** Match 5 real-world scenarios to the correct dispersion term (spread, dispersion, volatility). ### Day 83: Distribution shape: symmetric distributions - Foundations * **Objective:** Build a solid conceptual understanding of *distribution shape: symmetric distributions*. * **Theory:** A symmetric distribution has matching shape on both sides of its center; mean, median, and mode coincide. * **Practice:** Summarize the concept in your own words and give one real-world example before moving to application. ### Day 84: Distribution shape: symmetric distributions - Applied Practice * **Objective:** Apply *distribution shape: symmetric distributions* to solve concrete problems and solidify intuition. * **Theory (recap):** A symmetric distribution has matching shape on both sides of its center; mean, median, and mode coincide. * **Practice:** Identify 3 real datasets that appear approximately symmetric and plot histograms to confirm. ### Day 85: Distribution shape: left skew - Foundations * **Objective:** Build a solid conceptual understanding of *distribution shape: left skew*. * **Theory:** Left (negative) skew has a longer tail on the left; the mean is pulled below the median. * **Practice:** Summarize the concept in your own words and give one real-world example before moving to application. ### Day 86: Distribution shape: left skew - Applied Practice * **Objective:** Apply *distribution shape: left skew* to solve concrete problems and solidify intuition. * **Theory (recap):** Left (negative) skew has a longer tail on the left; the mean is pulled below the median. * **Practice:** Find a real dataset with left skew (e.g. age at retirement) and explain the tail's cause. ### Day 87: Distribution shape: right skew - Foundations * **Objective:** Build a solid conceptual understanding of *distribution shape: right skew*. * **Theory:** Right (positive) skew has a longer tail on the right; the mean is pulled above the median (e.g. income). * **Practice:** Summarize the concept in your own words and give one real-world example before moving to application. ### Day 88: Distribution shape: right skew - Applied Practice * **Objective:** Apply *distribution shape: right skew* to solve concrete problems and solidify intuition. * **Theory (recap):** Right (positive) skew has a longer tail on the right; the mean is pulled above the median (e.g. income). * **Practice:** Find a real dataset with right skew and compare its mean and median numerically. ### Day 89: Heavy-tailed distributions - Foundations * **Objective:** Build a solid conceptual understanding of *heavy-tailed distributions*. * **Theory:** Heavy tails mean extreme values occur more often than a Normal distribution would predict (e.g. stock returns, insurance claims). * **Practice:** Summarize the concept in your own words and give one real-world example before moving to application. ### Day 90: Heavy-tailed distributions - Applied Practice * **Objective:** Apply *heavy-tailed distributions* to solve concrete problems and solidify intuition. * **Theory (recap):** Heavy tails mean extreme values occur more often than a Normal distribution would predict (e.g. stock returns, insurance claims). * **Practice:** Compare a Normal-generated sample to a heavy-tailed sample (e.g. Student-t with low df) visually. ### Day 91: Skewness (quantitative measure) - Introduction * **Objective:** Grasp the core intuition behind *skewness (quantitative measure)* before the mechanics. * **Theory:** Skewness is a numeric measure of asymmetry; positive skewness indicates a right tail, negative indicates a left tail. * **Practice:** Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences. ### Day 92: Skewness (quantitative measure) - Deep Dive * **Objective:** Understand the full mechanics/derivation behind *skewness (quantitative measure)*. * **Theory:** Skewness is a numeric measure of asymmetry; positive skewness indicates a right tail, negative indicates a left tail. * **Practice:** Derive or re-derive the key formula/result by hand, step by step. ### Day 93: Skewness (quantitative measure) - Applied Practice * **Objective:** Apply *skewness (quantitative measure)* to a concrete problem or dataset. * **Theory (recap):** Skewness is a numeric measure of asymmetry; positive skewness indicates a right tail, negative indicates a left tail. * **Practice:** Compute skewness for 3 datasets and match the sign/magnitude to the histogram shape. ### Day 94: Kurtosis - Introduction * **Objective:** Grasp the core intuition behind *kurtosis* before the mechanics. * **Theory:** Kurtosis measures tail heaviness/peakedness relative to a Normal distribution; excess kurtosis of 0 means Normal-like tails. * **Practice:** Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences. ### Day 95: Kurtosis - Deep Dive * **Objective:** Understand the full mechanics/derivation behind *kurtosis*. * **Theory:** Kurtosis measures tail heaviness/peakedness relative to a Normal distribution; excess kurtosis of 0 means Normal-like tails. * **Practice:** Derive or re-derive the key formula/result by hand, step by step. ### Day 96: Kurtosis - Applied Practice * **Objective:** Apply *kurtosis* to a concrete problem or dataset. * **Theory (recap):** Kurtosis measures tail heaviness/peakedness relative to a Normal distribution; excess kurtosis of 0 means Normal-like tails. * **Practice:** Compute kurtosis for a Normal sample and a heavy-tailed sample and compare. ### Day 97: Practice: full descriptive statistics report * **Objective:** Understand and internalize *practice: full descriptive statistics report*. * **Theory:** Combine all descriptive measures into a single coherent summary of a dataset. * **Practice:** Write a one-page descriptive statistics report (mean, median, SD, skew, kurtosis, plots) for a public dataset. ## PHASE 2 - PROBABILITY ### Day 98: Sample space and events - Foundations * **Objective:** Build a solid conceptual understanding of *sample space and events*. * **Theory:** The sample space is the set of all possible outcomes; an event is any subset of that sample space. * **Practice:** Summarize the concept in your own words and give one real-world example before moving to application. ### Day 99: Sample space and events - Applied Practice * **Objective:** Apply *sample space and events* to solve concrete problems and solidify intuition. * **Theory (recap):** The sample space is the set of all possible outcomes; an event is any subset of that sample space. * **Practice:** Define the sample space and 3 events for rolling two dice. ### Day 100: Probability axioms - Foundations * **Objective:** Build a solid conceptual understanding of *probability axioms*. * **Theory:** Kolmogorov's axioms: probabilities are non-negative, the sample space has probability 1, and probabilities of disjoint events add. * **Practice:** Summarize the concept in your own words and give one real-world example before moving to application. ### Day 101: Probability axioms - Applied Practice * **Objective:** Apply *probability axioms* to solve concrete problems and solidify intuition. * **Theory (recap):** Kolmogorov's axioms: probabilities are non-negative, the sample space has probability 1, and probabilities of disjoint events add. * **Practice:** Verify the axioms hold for a simple dice/card example. ### Day 102: Counting principles/combinatorics basics - Foundations * **Objective:** Build a solid conceptual understanding of *counting principles/combinatorics basics*. * **Theory:** The multiplication principle counts outcomes of sequential independent choices. * **Practice:** Summarize the concept in your own words and give one real-world example before moving to application. ### Day 103: Counting principles/combinatorics basics - Applied Practice * **Objective:** Apply *counting principles/combinatorics basics* to solve concrete problems and solidify intuition. * **Theory (recap):** The multiplication principle counts outcomes of sequential independent choices. * **Practice:** Count the number of possible passwords under given length/character rules. ### Day 104: Permutations - Foundations * **Objective:** Build a solid conceptual understanding of *permutations*. * **Theory:** Permutations count ordered arrangements of items; order matters (nPr = n!/(n-r)!). * **Practice:** Summarize the concept in your own words and give one real-world example before moving to application. ### Day 105: Permutations - Applied Practice * **Objective:** Apply *permutations* to solve concrete problems and solidify intuition. * **Theory (recap):** Permutations count ordered arrangements of items; order matters (nPr = n!/(n-r)!). * **Practice:** Compute the number of ways to arrange 5 books on a shelf, and 3 out of 5 books in order. ### Day 106: Combinations - Introduction * **Objective:** Grasp the core intuition behind *combinations* before the mechanics. * **Theory:** Combinations count unordered selections of items; order does not matter (nCr = n!/(r!(n-r)!)). * **Practice:** Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences. ### Day 107: Combinations - Deep Dive * **Objective:** Understand the full mechanics/derivation behind *combinations*. * **Theory:** Combinations count unordered selections of items; order does not matter (nCr = n!/(r!(n-r)!)). * **Practice:** Derive or re-derive the key formula/result by hand, step by step. ### Day 108: Combinations - Applied Practice * **Objective:** Apply *combinations* to a concrete problem or dataset. * **Theory (recap):** Combinations count unordered selections of items; order does not matter (nCr = n!/(r!(n-r)!)). * **Practice:** Compute the number of ways to choose 3 people from a group of 10 for a committee. ### Day 109: Conditional probability - Introduction * **Objective:** Grasp the core intuition behind *conditional probability* before the mechanics. * **Theory:** Conditional probability P(A|B) = P(A and B)/P(B) updates the probability of A given that B has occurred. * **Practice:** Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences. ### Day 110: Conditional probability - Deep Dive * **Objective:** Understand the full mechanics/derivation behind *conditional probability*. * **Theory:** Conditional probability P(A|B) = P(A and B)/P(B) updates the probability of A given that B has occurred. * **Practice:** Derive or re-derive the key formula/result by hand, step by step. ### Day 111: Conditional probability - Applied Practice * **Objective:** Apply *conditional probability* to a concrete problem or dataset. * **Theory (recap):** Conditional probability P(A|B) = P(A and B)/P(B) updates the probability of A given that B has occurred. * **Practice:** Compute conditional probabilities from a 2x2 contingency table of disease/test results. ### Day 112: Law of total probability - Foundations * **Objective:** Build a solid conceptual understanding of *law of total probability*. * **Theory:** The law of total probability decomposes an event's probability across a partition of the sample space. * **Practice:** Summarize the concept in your own words and give one real-world example before moving to application. ### Day 113: Law of total probability - Applied Practice * **Objective:** Apply *law of total probability* to solve concrete problems and solidify intuition. * **Theory (recap):** The law of total probability decomposes an event's probability across a partition of the sample space. * **Practice:** Use the law of total probability to compute the overall defect rate across 3 factories. ### Day 114: Bayes' theorem: derivation - Introduction * **Objective:** Grasp the core intuition behind *bayes' theorem: derivation* before the mechanics. * **Theory:** Bayes' theorem inverts conditional probability: P(A|B) = P(B|A)P(A)/P(B), derived directly from the definition of conditional probability. * **Practice:** Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences. ### Day 115: Bayes' theorem: derivation - Deep Dive * **Objective:** Understand the full mechanics/derivation behind *bayes' theorem: derivation*. * **Theory:** Bayes' theorem inverts conditional probability: P(A|B) = P(B|A)P(A)/P(B), derived directly from the definition of conditional probability. * **Practice:** Derive or re-derive the key formula/result by hand, step by step. ### Day 116: Bayes' theorem: derivation - Applied Practice * **Objective:** Apply *bayes' theorem: derivation* to a concrete problem or dataset. * **Theory (recap):** Bayes' theorem inverts conditional probability: P(A|B) = P(B|A)P(A)/P(B), derived directly from the definition of conditional probability. * **Practice:** Derive Bayes' theorem from scratch starting from the definition of conditional probability. ### Day 117: Bayes' theorem: prior, likelihood, posterior - Introduction * **Objective:** Grasp the core intuition behind *bayes' theorem: prior, likelihood, posterior* before the mechanics. * **Theory:** Prior encodes belief before evidence, likelihood is how probable the evidence is given a hypothesis, posterior updates belief after evidence. * **Practice:** Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences. ### Day 118: Bayes' theorem: prior, likelihood, posterior - Deep Dive * **Objective:** Understand the full mechanics/derivation behind *bayes' theorem: prior, likelihood, posterior*. * **Theory:** Prior encodes belief before evidence, likelihood is how probable the evidence is given a hypothesis, posterior updates belief after evidence. * **Practice:** Derive or re-derive the key formula/result by hand, step by step. ### Day 119: Bayes' theorem: prior, likelihood, posterior - Applied Practice * **Objective:** Apply *bayes' theorem: prior, likelihood, posterior* to a concrete problem or dataset. * **Theory (recap):** Prior encodes belief before evidence, likelihood is how probable the evidence is given a hypothesis, posterior updates belief after evidence. * **Practice:** Solve the classic medical-test Bayes problem and correctly interpret the counter-intuitive result. ### Day 120: Independence of events - Foundations * **Objective:** Build a solid conceptual understanding of *independence of events*. * **Theory:** Two events are independent if P(A and B) = P(A)P(B); knowing one gives no information about the other. * **Practice:** Summarize the concept in your own words and give one real-world example before moving to application. ### Day 121: Independence of events - Applied Practice * **Objective:** Apply *independence of events* to solve concrete problems and solidify intuition. * **Theory (recap):** Two events are independent if P(A and B) = P(A)P(B); knowing one gives no information about the other. * **Practice:** Test whether two events in a dataset (e.g. gender and product choice) are statistically independent. ### Day 122: Mutually exclusive vs independent: common confusion - Foundations * **Objective:** Build a solid conceptual understanding of *mutually exclusive vs independent: common confusion*. * **Theory:** Mutually exclusive events cannot both happen (and are therefore strongly dependent); independent events can co-occur freely. * **Practice:** Summarize the concept in your own words and give one real-world example before moving to application. ### Day 123: Mutually exclusive vs independent: common confusion - Applied Practice * **Objective:** Apply *mutually exclusive vs independent: common confusion* to solve concrete problems and solidify intuition. * **Theory (recap):** Mutually exclusive events cannot both happen (and are therefore strongly dependent); independent events can co-occur freely. * **Practice:** Give 2 examples each of mutually exclusive and independent events and explain the difference. ### Day 124: Random variables: discrete - Foundations * **Objective:** Build a solid conceptual understanding of *random variables: discrete*. * **Theory:** A discrete random variable takes countable values, each with an associated probability mass. * **Practice:** Summarize the concept in your own words and give one real-world example before moving to application. ### Day 125: Random variables: discrete - Applied Practice * **Objective:** Apply *random variables: discrete* to solve concrete problems and solidify intuition. * **Theory (recap):** A discrete random variable takes countable values, each with an associated probability mass. * **Practice:** Define a discrete random variable for the outcome of rolling a die and list its distribution. ### Day 126: Random variables: continuous - Foundations * **Objective:** Build a solid conceptual understanding of *random variables: continuous*. * **Theory:** A continuous random variable takes uncountably many values; probability is described by a density, not a mass. * **Practice:** Summarize the concept in your own words and give one real-world example before moving to application. ### Day 127: Random variables: continuous - Applied Practice * **Objective:** Apply *random variables: continuous* to solve concrete problems and solidify intuition. * **Theory (recap):** A continuous random variable takes uncountably many values; probability is described by a density, not a mass. * **Practice:** Explain why P(X = exact value) = 0 for a continuous random variable. ### Day 128: Probability mass function (PMF) - Foundations * **Objective:** Build a solid conceptual understanding of *probability mass function (pmf)*. * **Theory:** The PMF gives the probability of each specific value for a discrete random variable. * **Practice:** Summarize the concept in your own words and give one real-world example before moving to application. ### Day 129: Probability mass function (PMF) - Applied Practice * **Objective:** Apply *probability mass function (pmf)* to solve concrete problems and solidify intuition. * **Theory (recap):** The PMF gives the probability of each specific value for a discrete random variable. * **Practice:** Plot the PMF of a Binomial(n=10, p=0.3) random variable. ### Day 130: Probability density function (PDF) - Introduction * **Objective:** Grasp the core intuition behind *probability density function (pdf)* before the mechanics. * **Theory:** The PDF describes relative likelihood for continuous variables; probability over an interval is the area under the curve. * **Practice:** Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences. ### Day 131: Probability density function (PDF) - Deep Dive * **Objective:** Understand the full mechanics/derivation behind *probability density function (pdf)*. * **Theory:** The PDF describes relative likelihood for continuous variables; probability over an interval is the area under the curve. * **Practice:** Derive or re-derive the key formula/result by hand, step by step. ### Day 132: Probability density function (PDF) - Applied Practice * **Objective:** Apply *probability density function (pdf)* to a concrete problem or dataset. * **Theory (recap):** The PDF describes relative likelihood for continuous variables; probability over an interval is the area under the curve. * **Practice:** Plot the PDF of a Normal(0,1) and shade the area representing P(-1 5-10 signals a problem. * **Practice:** Summarize the concept in your own words and give one real-world example before moving to application. ### Day 322: Variance Inflation Factor (VIF) - Applied Practice * **Objective:** Apply *variance inflation factor (vif)* to solve concrete problems and solidify intuition. * **Theory (recap):** VIF quantifies how much a coefficient's variance is inflated due to multicollinearity; VIF > 5-10 signals a problem. * **Practice:** Compute VIF for each predictor in a multiple regression and decide which to drop or combine. ### Day 323: Robust regression: Huber loss - Foundations * **Objective:** Build a solid conceptual understanding of *robust regression: huber loss*. * **Theory:** Huber loss blends squared error and absolute error, reducing the influence of outliers compared to standard least squares. * **Practice:** Summarize the concept in your own words and give one real-world example before moving to application. ### Day 324: Robust regression: Huber loss - Applied Practice * **Objective:** Apply *robust regression: huber loss* to solve concrete problems and solidify intuition. * **Theory (recap):** Huber loss blends squared error and absolute error, reducing the influence of outliers compared to standard least squares. * **Practice:** Fit an OLS and a Huber-loss regression on data with outliers and compare coefficient stability. ### Day 325: Robust regression: RANSAC - Introduction * **Objective:** Grasp the core intuition behind *robust regression: ransac* before the mechanics. * **Theory:** RANSAC iteratively fits models to random subsets to find a fit robust to a large fraction of outliers. * **Practice:** Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences. ### Day 326: Robust regression: RANSAC - Deep Dive * **Objective:** Understand the full mechanics/derivation behind *robust regression: ransac*. * **Theory:** RANSAC iteratively fits models to random subsets to find a fit robust to a large fraction of outliers. * **Practice:** Derive or re-derive the key formula/result by hand, step by step. ### Day 327: Robust regression: RANSAC - Applied Practice * **Objective:** Apply *robust regression: ransac* to a concrete problem or dataset. * **Theory (recap):** RANSAC iteratively fits models to random subsets to find a fit robust to a large fraction of outliers. * **Practice:** Apply RANSAC regression to a dataset with heavy contamination and compare to OLS. ### Day 328: Quantile regression - Foundations * **Objective:** Build a solid conceptual understanding of *quantile regression*. * **Theory:** Quantile regression models conditional quantiles (e.g. the median) of Y given X, rather than just the conditional mean. * **Practice:** Summarize the concept in your own words and give one real-world example before moving to application. ### Day 329: Quantile regression - Applied Practice * **Objective:** Apply *quantile regression* to solve concrete problems and solidify intuition. * **Theory (recap):** Quantile regression models conditional quantiles (e.g. the median) of Y given X, rather than just the conditional mean. * **Practice:** Fit a median (quantile=0.5) regression alongside OLS and compare on skewed data. ### Day 330: Generalized Linear Models: concept - Foundations * **Objective:** Build a solid conceptual understanding of *generalized linear models: concept*. * **Theory:** GLMs extend linear regression to non-Normal outcomes via a link function and an appropriate error distribution. * **Practice:** Summarize the concept in your own words and give one real-world example before moving to application. ### Day 331: Generalized Linear Models: concept - Applied Practice * **Objective:** Apply *generalized linear models: concept* to solve concrete problems and solidify intuition. * **Theory (recap):** GLMs extend linear regression to non-Normal outcomes via a link function and an appropriate error distribution. * **Practice:** Explain, in your own words, how a GLM generalizes OLS using a link function. ### Day 332: Logistic regression - Introduction * **Objective:** Grasp the core intuition behind *logistic regression* before the mechanics. * **Theory:** Logistic regression models the log-odds of a binary outcome as a linear function of predictors. * **Practice:** Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences. ### Day 333: Logistic regression - Deep Dive * **Objective:** Understand the full mechanics/derivation behind *logistic regression*. * **Theory:** Logistic regression models the log-odds of a binary outcome as a linear function of predictors. * **Practice:** Derive or re-derive the key formula/result by hand, step by step. ### Day 334: Logistic regression - Applied Practice * **Objective:** Apply *logistic regression* to a concrete problem or dataset. * **Theory (recap):** Logistic regression models the log-odds of a binary outcome as a linear function of predictors. * **Practice:** Fit a logistic regression on a binary-outcome dataset and interpret coefficients as odds ratios. ### Day 335: Poisson regression - Introduction * **Objective:** Grasp the core intuition behind *poisson regression* before the mechanics. * **Theory:** Poisson regression models count outcomes, assuming the log of the expected count is linear in the predictors. * **Practice:** Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences. ### Day 336: Poisson regression - Deep Dive * **Objective:** Understand the full mechanics/derivation behind *poisson regression*. * **Theory:** Poisson regression models count outcomes, assuming the log of the expected count is linear in the predictors. * **Practice:** Derive or re-derive the key formula/result by hand, step by step. ### Day 337: Poisson regression - Applied Practice * **Objective:** Apply *poisson regression* to a concrete problem or dataset. * **Theory (recap):** Poisson regression models count outcomes, assuming the log of the expected count is linear in the predictors. * **Practice:** Fit a Poisson regression on count data (e.g. number of customer complaints) and interpret coefficients. ### Day 338: Practice: full regression workflow * **Objective:** Understand and internalize *practice: full regression workflow*. * **Theory:** Combine model fitting, diagnostics, and interpretation into one complete regression analysis. * **Practice:** Perform a full regression analysis on a real dataset: fit, diagnose, refine, and report results. ## PHASE 6 - EXPERIMENTAL DESIGN ### Day 339: A/B testing: fundamentals - Foundations * **Objective:** Build a solid conceptual understanding of *a/b testing: fundamentals*. * **Theory:** A/B testing randomly assigns users to control and treatment groups to estimate the causal effect of a change. * **Practice:** Summarize the concept in your own words and give one real-world example before moving to application. ### Day 340: A/B testing: fundamentals - Applied Practice * **Objective:** Apply *a/b testing: fundamentals* to solve concrete problems and solidify intuition. * **Theory (recap):** A/B testing randomly assigns users to control and treatment groups to estimate the causal effect of a change. * **Practice:** Design an A/B test plan for a hypothetical website change, specifying metric and hypotheses. ### Day 341: Randomization - Foundations * **Objective:** Build a solid conceptual understanding of *randomization*. * **Theory:** Randomization balances known and unknown confounders across groups, enabling causal interpretation of the comparison. * **Practice:** Summarize the concept in your own words and give one real-world example before moving to application. ### Day 342: Randomization - Applied Practice * **Objective:** Apply *randomization* to solve concrete problems and solidify intuition. * **Theory (recap):** Randomization balances known and unknown confounders across groups, enabling causal interpretation of the comparison. * **Practice:** Explain why randomization, not just a large sample, is essential for causal claims in an experiment. ### Day 343: Sample size calculation for A/B tests - Introduction * **Objective:** Grasp the core intuition behind *sample size calculation for a/b tests* before the mechanics. * **Theory:** Sample size for an A/B test depends on baseline rate, minimum detectable effect, significance level, and power. * **Practice:** Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences. ### Day 344: Sample size calculation for A/B tests - Deep Dive * **Objective:** Understand the full mechanics/derivation behind *sample size calculation for a/b tests*. * **Theory:** Sample size for an A/B test depends on baseline rate, minimum detectable effect, significance level, and power. * **Practice:** Derive or re-derive the key formula/result by hand, step by step. ### Day 345: Sample size calculation for A/B tests - Applied Practice * **Objective:** Apply *sample size calculation for a/b tests* to a concrete problem or dataset. * **Theory (recap):** Sample size for an A/B test depends on baseline rate, minimum detectable effect, significance level, and power. * **Practice:** Calculate the required sample size for an A/B test given a baseline conversion rate and target MDE. ### Day 346: Design of experiments: factorial design - Introduction * **Objective:** Grasp the core intuition behind *design of experiments: factorial design* before the mechanics. * **Theory:** Factorial designs test multiple factors simultaneously, allowing estimation of main effects and interactions efficiently. * **Practice:** Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences. ### Day 347: Design of experiments: factorial design - Deep Dive * **Objective:** Understand the full mechanics/derivation behind *design of experiments: factorial design*. * **Theory:** Factorial designs test multiple factors simultaneously, allowing estimation of main effects and interactions efficiently. * **Practice:** Derive or re-derive the key formula/result by hand, step by step. ### Day 348: Design of experiments: factorial design - Applied Practice * **Objective:** Apply *design of experiments: factorial design* to a concrete problem or dataset. * **Theory (recap):** Factorial designs test multiple factors simultaneously, allowing estimation of main effects and interactions efficiently. * **Practice:** Design a 2x2 factorial experiment testing two factors and list all treatment combinations. ### Day 349: Blocking - Foundations * **Objective:** Build a solid conceptual understanding of *blocking*. * **Theory:** Blocking groups similar experimental units together to reduce the influence of a known nuisance variable. * **Practice:** Summarize the concept in your own words and give one real-world example before moving to application. ### Day 350: Blocking - Applied Practice * **Objective:** Apply *blocking* to solve concrete problems and solidify intuition. * **Theory (recap):** Blocking groups similar experimental units together to reduce the influence of a known nuisance variable. * **Practice:** Design a blocked experiment controlling for a nuisance factor (e.g. time of day). ### Day 351: Latin square design - Foundations * **Objective:** Build a solid conceptual understanding of *latin square design*. * **Theory:** A Latin square design controls for two nuisance factors simultaneously using a structured grid layout. * **Practice:** Summarize the concept in your own words and give one real-world example before moving to application. ### Day 352: Latin square design - Applied Practice * **Objective:** Apply *latin square design* to solve concrete problems and solidify intuition. * **Theory (recap):** A Latin square design controls for two nuisance factors simultaneously using a structured grid layout. * **Practice:** Construct a Latin square design for an experiment with two blocking factors. ### Day 353: ANOVA: decomposition of variance - Introduction * **Objective:** Grasp the core intuition behind *anova: decomposition of variance* before the mechanics. * **Theory:** ANOVA decomposes total variance into between-group and within-group components to test for differences among group means. * **Practice:** Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences. ### Day 354: ANOVA: decomposition of variance - Deep Dive * **Objective:** Understand the full mechanics/derivation behind *anova: decomposition of variance*. * **Theory:** ANOVA decomposes total variance into between-group and within-group components to test for differences among group means. * **Practice:** Derive or re-derive the key formula/result by hand, step by step. ### Day 355: ANOVA: decomposition of variance - Applied Practice * **Objective:** Apply *anova: decomposition of variance* to a concrete problem or dataset. * **Theory (recap):** ANOVA decomposes total variance into between-group and within-group components to test for differences among group means. * **Practice:** Manually decompose total sum of squares into between- and within-group components for a small dataset. ### Day 356: One-way ANOVA - Introduction * **Objective:** Grasp the core intuition behind *one-way anova* before the mechanics. * **Theory:** One-way ANOVA tests whether means differ across 3+ groups defined by a single factor. * **Practice:** Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences. ### Day 357: One-way ANOVA - Deep Dive * **Objective:** Understand the full mechanics/derivation behind *one-way anova*. * **Theory:** One-way ANOVA tests whether means differ across 3+ groups defined by a single factor. * **Practice:** Derive or re-derive the key formula/result by hand, step by step. ### Day 358: One-way ANOVA - Applied Practice * **Objective:** Apply *one-way anova* to a concrete problem or dataset. * **Theory (recap):** One-way ANOVA tests whether means differ across 3+ groups defined by a single factor. * **Practice:** Run a one-way ANOVA on a 3-group dataset and interpret the F-statistic and p-value. ### Day 359: Two-way ANOVA - Foundations * **Objective:** Build a solid conceptual understanding of *two-way anova*. * **Theory:** Two-way ANOVA tests the effects of two factors and their interaction simultaneously. * **Practice:** Summarize the concept in your own words and give one real-world example before moving to application. ### Day 360: Two-way ANOVA - Applied Practice * **Objective:** Apply *two-way anova* to solve concrete problems and solidify intuition. * **Theory (recap):** Two-way ANOVA tests the effects of two factors and their interaction simultaneously. * **Practice:** Run a two-way ANOVA and interpret both main effects and the interaction effect. ### Day 361: Post-hoc tests (Tukey HSD) - Foundations * **Objective:** Build a solid conceptual understanding of *post-hoc tests (tukey hsd)*. * **Theory:** Post-hoc tests like Tukey HSD identify which specific group pairs differ after a significant ANOVA result. * **Practice:** Summarize the concept in your own words and give one real-world example before moving to application. ### Day 362: Post-hoc tests (Tukey HSD) - Applied Practice * **Objective:** Apply *post-hoc tests (tukey hsd)* to solve concrete problems and solidify intuition. * **Theory (recap):** Post-hoc tests like Tukey HSD identify which specific group pairs differ after a significant ANOVA result. * **Practice:** Apply Tukey HSD after a significant one-way ANOVA and identify which group pairs differ. ### Day 363: Chi-square goodness-of-fit test - Introduction * **Objective:** Grasp the core intuition behind *chi-square goodness-of-fit test* before the mechanics. * **Theory:** The goodness-of-fit test checks whether observed categorical frequencies match an expected distribution. * **Practice:** Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences. ### Day 364: Chi-square goodness-of-fit test - Deep Dive * **Objective:** Understand the full mechanics/derivation behind *chi-square goodness-of-fit test*. * **Theory:** The goodness-of-fit test checks whether observed categorical frequencies match an expected distribution. * **Practice:** Derive or re-derive the key formula/result by hand, step by step. ### Day 365: Chi-square goodness-of-fit test - Applied Practice * **Objective:** Apply *chi-square goodness-of-fit test* to a concrete problem or dataset. * **Theory (recap):** The goodness-of-fit test checks whether observed categorical frequencies match an expected distribution. * **Practice:** Run a chi-square goodness-of-fit test on dice-roll data against a uniform expectation. ### Day 366: Chi-square test of independence - Foundations * **Objective:** Build a solid conceptual understanding of *chi-square test of independence*. * **Theory:** The test of independence checks whether two categorical variables are associated using a contingency table. * **Practice:** Summarize the concept in your own words and give one real-world example before moving to application. ### Day 367: Chi-square test of independence - Applied Practice * **Objective:** Apply *chi-square test of independence* to solve concrete problems and solidify intuition. * **Theory (recap):** The test of independence checks whether two categorical variables are associated using a contingency table. * **Practice:** Run a chi-square test of independence on a 2x2 contingency table (e.g. treatment vs outcome). ### Day 368: Practice: designing and analyzing an experiment * **Objective:** Understand and internalize *practice: designing and analyzing an experiment*. * **Theory:** Integrate design principles and the appropriate statistical test into one complete experiment. * **Practice:** Design, simulate, and analyze a full experiment from hypothesis to conclusion. ## PHASE 7 - MULTIVARIATE STATISTICS ### Day 369: PCA: covariance matrix - Foundations * **Objective:** Build a solid conceptual understanding of *pca: covariance matrix*. * **Theory:** PCA begins by computing the covariance matrix of standardized variables, capturing how features co-vary. * **Practice:** Summarize the concept in your own words and give one real-world example before moving to application. ### Day 370: PCA: covariance matrix - Applied Practice * **Objective:** Apply *pca: covariance matrix* to solve concrete problems and solidify intuition. * **Theory (recap):** PCA begins by computing the covariance matrix of standardized variables, capturing how features co-vary. * **Practice:** Compute the covariance matrix for a multi-feature dataset and inspect it for strong relationships. ### Day 371: PCA: eigenvectors and variance explained - Introduction * **Objective:** Grasp the core intuition behind *pca: eigenvectors and variance explained* before the mechanics. * **Theory:** Principal components are the eigenvectors of the covariance matrix, ordered by the variance (eigenvalue) they explain. * **Practice:** Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences. ### Day 372: PCA: eigenvectors and variance explained - Deep Dive * **Objective:** Understand the full mechanics/derivation behind *pca: eigenvectors and variance explained*. * **Theory:** Principal components are the eigenvectors of the covariance matrix, ordered by the variance (eigenvalue) they explain. * **Practice:** Derive or re-derive the key formula/result by hand, step by step. ### Day 373: PCA: eigenvectors and variance explained - Applied Practice * **Objective:** Apply *pca: eigenvectors and variance explained* to a concrete problem or dataset. * **Theory (recap):** Principal components are the eigenvectors of the covariance matrix, ordered by the variance (eigenvalue) they explain. * **Practice:** Perform PCA on a dataset and plot the proportion of variance explained by each component. ### Day 374: PCA: practice - Foundations * **Objective:** Build a solid conceptual understanding of *pca: practice*. * **Theory:** Apply PCA for dimensionality reduction on a real, moderately high-dimensional dataset. * **Practice:** Summarize the concept in your own words and give one real-world example before moving to application. ### Day 375: PCA: practice - Applied Practice * **Objective:** Apply *pca: practice* to solve concrete problems and solidify intuition. * **Theory (recap):** Apply PCA for dimensionality reduction on a real, moderately high-dimensional dataset. * **Practice:** Reduce a dataset to 2 principal components and visualize the result, labeling by a known category. ### Day 376: Factor Analysis: latent variables - Introduction * **Objective:** Grasp the core intuition behind *factor analysis: latent variables* before the mechanics. * **Theory:** Factor Analysis assumes observed correlations arise from a smaller number of unobserved latent factors. * **Practice:** Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences. ### Day 377: Factor Analysis: latent variables - Deep Dive * **Objective:** Understand the full mechanics/derivation behind *factor analysis: latent variables*. * **Theory:** Factor Analysis assumes observed correlations arise from a smaller number of unobserved latent factors. * **Practice:** Derive or re-derive the key formula/result by hand, step by step. ### Day 378: Factor Analysis: latent variables - Applied Practice * **Objective:** Apply *factor analysis: latent variables* to a concrete problem or dataset. * **Theory (recap):** Factor Analysis assumes observed correlations arise from a smaller number of unobserved latent factors. * **Practice:** Run exploratory factor analysis on a survey dataset and interpret the resulting factors. ### Day 379: Factor Analysis: practice - Foundations * **Objective:** Build a solid conceptual understanding of *factor analysis: practice*. * **Theory:** Compare and contrast the practical output of Factor Analysis against PCA on the same data. * **Practice:** Summarize the concept in your own words and give one real-world example before moving to application. ### Day 380: Factor Analysis: practice - Applied Practice * **Objective:** Apply *factor analysis: practice* to solve concrete problems and solidify intuition. * **Theory (recap):** Compare and contrast the practical output of Factor Analysis against PCA on the same data. * **Practice:** Run PCA and Factor Analysis on the same dataset and compare the resulting components/factors. ### Day 381: K-means clustering - Introduction * **Objective:** Grasp the core intuition behind *k-means clustering* before the mechanics. * **Theory:** K-means partitions data into k clusters by iteratively minimizing within-cluster variance around centroids. * **Practice:** Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences. ### Day 382: K-means clustering - Deep Dive * **Objective:** Understand the full mechanics/derivation behind *k-means clustering*. * **Theory:** K-means partitions data into k clusters by iteratively minimizing within-cluster variance around centroids. * **Practice:** Derive or re-derive the key formula/result by hand, step by step. ### Day 383: K-means clustering - Applied Practice * **Objective:** Apply *k-means clustering* to a concrete problem or dataset. * **Theory (recap):** K-means partitions data into k clusters by iteratively minimizing within-cluster variance around centroids. * **Practice:** Run K-means on a dataset, choose k using the elbow method, and visualize the clusters. ### Day 384: Hierarchical clustering - Foundations * **Objective:** Build a solid conceptual understanding of *hierarchical clustering*. * **Theory:** Hierarchical clustering builds a tree (dendrogram) of nested clusters via agglomerative or divisive merging. * **Practice:** Summarize the concept in your own words and give one real-world example before moving to application. ### Day 385: Hierarchical clustering - Applied Practice * **Objective:** Apply *hierarchical clustering* to solve concrete problems and solidify intuition. * **Theory (recap):** Hierarchical clustering builds a tree (dendrogram) of nested clusters via agglomerative or divisive merging. * **Practice:** Build a dendrogram for a small dataset and choose a cut point to define clusters. ### Day 386: Clustering evaluation metrics - Foundations * **Objective:** Build a solid conceptual understanding of *clustering evaluation metrics*. * **Theory:** Metrics like silhouette score and within-cluster sum of squares assess clustering quality without ground-truth labels. * **Practice:** Summarize the concept in your own words and give one real-world example before moving to application. ### Day 387: Clustering evaluation metrics - Applied Practice * **Objective:** Apply *clustering evaluation metrics* to solve concrete problems and solidify intuition. * **Theory (recap):** Metrics like silhouette score and within-cluster sum of squares assess clustering quality without ground-truth labels. * **Practice:** Compute the silhouette score for K-means results across different values of k. ### Day 388: Multivariate regression - Introduction * **Objective:** Grasp the core intuition behind *multivariate regression* before the mechanics. * **Theory:** Multivariate regression models multiple dependent variables simultaneously as functions of the same predictors. * **Practice:** Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences. ### Day 389: Multivariate regression - Deep Dive * **Objective:** Understand the full mechanics/derivation behind *multivariate regression*. * **Theory:** Multivariate regression models multiple dependent variables simultaneously as functions of the same predictors. * **Practice:** Derive or re-derive the key formula/result by hand, step by step. ### Day 390: Multivariate regression - Applied Practice * **Objective:** Apply *multivariate regression* to a concrete problem or dataset. * **Theory (recap):** Multivariate regression models multiple dependent variables simultaneously as functions of the same predictors. * **Practice:** Fit a multivariate regression with two dependent variables and interpret the coefficient matrix. ### Day 391: MANOVA - Foundations * **Objective:** Build a solid conceptual understanding of *manova*. * **Theory:** MANOVA extends ANOVA to test differences in group means across multiple dependent variables jointly. * **Practice:** Summarize the concept in your own words and give one real-world example before moving to application. ### Day 392: MANOVA - Applied Practice * **Objective:** Apply *manova* to solve concrete problems and solidify intuition. * **Theory (recap):** MANOVA extends ANOVA to test differences in group means across multiple dependent variables jointly. * **Practice:** Run a MANOVA comparing groups on two correlated outcome variables simultaneously. ### Day 393: Canonical correlation analysis - Foundations * **Objective:** Build a solid conceptual understanding of *canonical correlation analysis*. * **Theory:** Canonical correlation finds linear combinations of two variable sets that are maximally correlated with each other. * **Practice:** Summarize the concept in your own words and give one real-world example before moving to application. ### Day 394: Canonical correlation analysis - Applied Practice * **Objective:** Apply *canonical correlation analysis* to solve concrete problems and solidify intuition. * **Theory (recap):** Canonical correlation finds linear combinations of two variable sets that are maximally correlated with each other. * **Practice:** Run canonical correlation analysis between two feature sets and interpret the leading canonical pair. ### Day 395: Practice: multivariate analysis on real dataset * **Objective:** Understand and internalize *practice: multivariate analysis on real dataset*. * **Theory:** Combine PCA/Factor Analysis and clustering into one integrated multivariate exploration. * **Practice:** Explore a real multivariate dataset end-to-end: reduce dimensions, cluster, and interpret results. ## PHASE 8 - BAYESIAN STATISTICS ### Day 396: Bayesian thinking: prior and posterior - Introduction * **Objective:** Grasp the core intuition behind *bayesian thinking: prior and posterior* before the mechanics. * **Theory:** Bayesian inference updates a prior belief into a posterior belief using observed data via Bayes' theorem. * **Practice:** Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences. ### Day 397: Bayesian thinking: prior and posterior - Deep Dive * **Objective:** Understand the full mechanics/derivation behind *bayesian thinking: prior and posterior*. * **Theory:** Bayesian inference updates a prior belief into a posterior belief using observed data via Bayes' theorem. * **Practice:** Derive or re-derive the key formula/result by hand, step by step. ### Day 398: Bayesian thinking: prior and posterior - Applied Practice * **Objective:** Apply *bayesian thinking: prior and posterior* to a concrete problem or dataset. * **Theory (recap):** Bayesian inference updates a prior belief into a posterior belief using observed data via Bayes' theorem. * **Practice:** Update a simple prior belief about a coin's fairness after observing 10 flips. ### Day 399: Choosing priors - Foundations * **Objective:** Build a solid conceptual understanding of *choosing priors*. * **Theory:** Priors can be informative (encoding real prior knowledge) or weakly informative/non-informative (letting the data dominate). * **Practice:** Summarize the concept in your own words and give one real-world example before moving to application. ### Day 400: Choosing priors - Applied Practice * **Objective:** Apply *choosing priors* to solve concrete problems and solidify intuition. * **Theory (recap):** Priors can be informative (encoding real prior knowledge) or weakly informative/non-informative (letting the data dominate). * **Practice:** Compare posteriors resulting from an informative vs a flat prior on the same data. ### Day 401: Conjugate priors: Beta-Binomial - Introduction * **Objective:** Grasp the core intuition behind *conjugate priors: beta-binomial* before the mechanics. * **Theory:** The Beta distribution is the conjugate prior for a Binomial likelihood, giving a closed-form Beta posterior. * **Practice:** Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences. ### Day 402: Conjugate priors: Beta-Binomial - Deep Dive * **Objective:** Understand the full mechanics/derivation behind *conjugate priors: beta-binomial*. * **Theory:** The Beta distribution is the conjugate prior for a Binomial likelihood, giving a closed-form Beta posterior. * **Practice:** Derive or re-derive the key formula/result by hand, step by step. ### Day 403: Conjugate priors: Beta-Binomial - Applied Practice * **Objective:** Apply *conjugate priors: beta-binomial* to a concrete problem or dataset. * **Theory (recap):** The Beta distribution is the conjugate prior for a Binomial likelihood, giving a closed-form Beta posterior. * **Practice:** Derive the Beta posterior update formula from a Beta prior and Binomial data by hand. ### Day 404: Conjugate priors: Gamma-Poisson - Introduction * **Objective:** Grasp the core intuition behind *conjugate priors: gamma-poisson* before the mechanics. * **Theory:** The Gamma distribution is the conjugate prior for a Poisson likelihood, giving a closed-form Gamma posterior. * **Practice:** Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences. ### Day 405: Conjugate priors: Gamma-Poisson - Deep Dive * **Objective:** Understand the full mechanics/derivation behind *conjugate priors: gamma-poisson*. * **Theory:** The Gamma distribution is the conjugate prior for a Poisson likelihood, giving a closed-form Gamma posterior. * **Practice:** Derive or re-derive the key formula/result by hand, step by step. ### Day 406: Conjugate priors: Gamma-Poisson - Applied Practice * **Objective:** Apply *conjugate priors: gamma-poisson* to a concrete problem or dataset. * **Theory (recap):** The Gamma distribution is the conjugate prior for a Poisson likelihood, giving a closed-form Gamma posterior. * **Practice:** Derive the Gamma posterior update formula for Poisson-distributed count data. ### Day 407: Markov Chain Monte Carlo: concept - Introduction * **Objective:** Grasp the core intuition behind *markov chain monte carlo: concept* before the mechanics. * **Theory:** MCMC generates samples from a posterior distribution that is too complex to compute analytically, by constructing a Markov chain whose stationary distribution is the posterior. * **Practice:** Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences. ### Day 408: Markov Chain Monte Carlo: concept - Deep Dive * **Objective:** Understand the full mechanics/derivation behind *markov chain monte carlo: concept*. * **Theory:** MCMC generates samples from a posterior distribution that is too complex to compute analytically, by constructing a Markov chain whose stationary distribution is the posterior. * **Practice:** Derive or re-derive the key formula/result by hand, step by step. ### Day 409: Markov Chain Monte Carlo: concept - Applied Practice * **Objective:** Apply *markov chain monte carlo: concept* to a concrete problem or dataset. * **Theory (recap):** MCMC generates samples from a posterior distribution that is too complex to compute analytically, by constructing a Markov chain whose stationary distribution is the posterior. * **Practice:** Explain in your own words why MCMC is needed when conjugate priors are unavailable. ### Day 410: Metropolis-Hastings algorithm - Introduction * **Objective:** Grasp the core intuition behind *metropolis-hastings algorithm* before the mechanics. * **Theory:** Metropolis-Hastings proposes new parameter values and accepts/rejects them based on a probability ratio to explore the posterior. * **Practice:** Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences. ### Day 411: Metropolis-Hastings algorithm - Deep Dive * **Objective:** Understand the full mechanics/derivation behind *metropolis-hastings algorithm*. * **Theory:** Metropolis-Hastings proposes new parameter values and accepts/rejects them based on a probability ratio to explore the posterior. * **Practice:** Derive or re-derive the key formula/result by hand, step by step. ### Day 412: Metropolis-Hastings algorithm - Applied Practice * **Objective:** Apply *metropolis-hastings algorithm* to a concrete problem or dataset. * **Theory (recap):** Metropolis-Hastings proposes new parameter values and accepts/rejects them based on a probability ratio to explore the posterior. * **Practice:** Implement a basic Metropolis-Hastings sampler from scratch for a simple 1-parameter model. ### Day 413: Gibbs sampling - Introduction * **Objective:** Grasp the core intuition behind *gibbs sampling* before the mechanics. * **Theory:** Gibbs sampling draws each parameter in turn from its full conditional distribution given the others, useful when those conditionals are known. * **Practice:** Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences. ### Day 414: Gibbs sampling - Deep Dive * **Objective:** Understand the full mechanics/derivation behind *gibbs sampling*. * **Theory:** Gibbs sampling draws each parameter in turn from its full conditional distribution given the others, useful when those conditionals are known. * **Practice:** Derive or re-derive the key formula/result by hand, step by step. ### Day 415: Gibbs sampling - Applied Practice * **Objective:** Apply *gibbs sampling* to a concrete problem or dataset. * **Theory (recap):** Gibbs sampling draws each parameter in turn from its full conditional distribution given the others, useful when those conditionals are known. * **Practice:** Implement Gibbs sampling for a simple two-parameter conjugate model. ### Day 416: Convergence diagnostics for MCMC - Foundations * **Objective:** Build a solid conceptual understanding of *convergence diagnostics for mcmc*. * **Theory:** Trace plots, R-hat, and effective sample size diagnose whether an MCMC chain has converged to the target distribution. * **Practice:** Summarize the concept in your own words and give one real-world example before moving to application. ### Day 417: Convergence diagnostics for MCMC - Applied Practice * **Objective:** Apply *convergence diagnostics for mcmc* to solve concrete problems and solidify intuition. * **Theory (recap):** Trace plots, R-hat, and effective sample size diagnose whether an MCMC chain has converged to the target distribution. * **Practice:** Run an MCMC chain and evaluate convergence using trace plots and R-hat. ### Day 418: Probabilistic programming: PyMC - Introduction * **Objective:** Grasp the core intuition behind *probabilistic programming: pymc* before the mechanics. * **Theory:** PyMC lets you specify Bayesian models declaratively and automatically handles sampling via MCMC/HMC. * **Practice:** Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences. ### Day 419: Probabilistic programming: PyMC - Deep Dive * **Objective:** Understand the full mechanics/derivation behind *probabilistic programming: pymc*. * **Theory:** PyMC lets you specify Bayesian models declaratively and automatically handles sampling via MCMC/HMC. * **Practice:** Derive or re-derive the key formula/result by hand, step by step. ### Day 420: Probabilistic programming: PyMC - Applied Practice * **Objective:** Apply *probabilistic programming: pymc* to a concrete problem or dataset. * **Theory (recap):** PyMC lets you specify Bayesian models declaratively and automatically handles sampling via MCMC/HMC. * **Practice:** Build and fit a simple Bayesian linear regression model in PyMC. ### Day 421: Probabilistic programming: Stan - Foundations * **Objective:** Build a solid conceptual understanding of *probabilistic programming: stan*. * **Theory:** Stan is a high-performance probabilistic programming language using Hamiltonian Monte Carlo for efficient sampling. * **Practice:** Summarize the concept in your own words and give one real-world example before moving to application. ### Day 422: Probabilistic programming: Stan - Applied Practice * **Objective:** Apply *probabilistic programming: stan* to solve concrete problems and solidify intuition. * **Theory (recap):** Stan is a high-performance probabilistic programming language using Hamiltonian Monte Carlo for efficient sampling. * **Practice:** Build and fit the same Bayesian model in Stan and compare results/runtime with PyMC. ### Day 423: Model comparison: AIC and BIC - Introduction * **Objective:** Grasp the core intuition behind *model comparison: aic and bic* before the mechanics. * **Theory:** AIC and BIC balance model fit against complexity, penalizing extra parameters to avoid overfitting when comparing models. * **Practice:** Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences. ### Day 424: Model comparison: AIC and BIC - Deep Dive * **Objective:** Understand the full mechanics/derivation behind *model comparison: aic and bic*. * **Theory:** AIC and BIC balance model fit against complexity, penalizing extra parameters to avoid overfitting when comparing models. * **Practice:** Derive or re-derive the key formula/result by hand, step by step. ### Day 425: Model comparison: AIC and BIC - Applied Practice * **Objective:** Apply *model comparison: aic and bic* to a concrete problem or dataset. * **Theory (recap):** AIC and BIC balance model fit against complexity, penalizing extra parameters to avoid overfitting when comparing models. * **Practice:** Compare 3 nested regression models using AIC and BIC and select the best one. ### Day 426: Model comparison: WAIC - Foundations * **Objective:** Build a solid conceptual understanding of *model comparison: waic*. * **Theory:** WAIC is a Bayesian, fully-generative alternative to AIC that uses the full posterior distribution rather than a point estimate. * **Practice:** Summarize the concept in your own words and give one real-world example before moving to application. ### Day 427: Model comparison: WAIC - Applied Practice * **Objective:** Apply *model comparison: waic* to solve concrete problems and solidify intuition. * **Theory (recap):** WAIC is a Bayesian, fully-generative alternative to AIC that uses the full posterior distribution rather than a point estimate. * **Practice:** Compute WAIC for two Bayesian models fit in PyMC and compare to AIC/BIC results. ### Day 428: Posterior predictive checks - Introduction * **Objective:** Grasp the core intuition behind *posterior predictive checks* before the mechanics. * **Theory:** Posterior predictive checks simulate new data from the fitted model and compare it to observed data to assess model fit. * **Practice:** Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences. ### Day 429: Posterior predictive checks - Deep Dive * **Objective:** Understand the full mechanics/derivation behind *posterior predictive checks*. * **Theory:** Posterior predictive checks simulate new data from the fitted model and compare it to observed data to assess model fit. * **Practice:** Derive or re-derive the key formula/result by hand, step by step. ### Day 430: Posterior predictive checks - Applied Practice * **Objective:** Apply *posterior predictive checks* to a concrete problem or dataset. * **Theory (recap):** Posterior predictive checks simulate new data from the fitted model and compare it to observed data to assess model fit. * **Practice:** Run posterior predictive checks on a fitted Bayesian model and visually assess fit quality. ### Day 431: Practice: full Bayesian analysis workflow * **Objective:** Understand and internalize *practice: full bayesian analysis workflow*. * **Theory:** Integrate prior specification, sampling, diagnostics, and model checking into one full Bayesian analysis. * **Practice:** Perform a complete Bayesian analysis on a real dataset from prior choice through posterior predictive checks. ## PHASE 9 - STATISTICAL COMPUTING ### Day 432: R: tidyverse fundamentals - Foundations * **Objective:** Build a solid conceptual understanding of *r: tidyverse fundamentals*. * **Theory:** The tidyverse is a coherent set of R packages built around tidy data principles (one row per observation, one column per variable). * **Practice:** Summarize the concept in your own words and give one real-world example before moving to application. ### Day 433: R: tidyverse fundamentals - Applied Practice * **Objective:** Apply *r: tidyverse fundamentals* to solve concrete problems and solidify intuition. * **Theory (recap):** The tidyverse is a coherent set of R packages built around tidy data principles (one row per observation, one column per variable). * **Practice:** Load a dataset in R and reshape it into tidy format using tidyr. ### Day 434: R: data manipulation with dplyr - Foundations * **Objective:** Build a solid conceptual understanding of *r: data manipulation with dplyr*. * **Theory:** dplyr provides verbs (filter, select, mutate, summarize, group\_by) for expressive, chainable data manipulation. * **Practice:** Summarize the concept in your own words and give one real-world example before moving to application. ### Day 435: R: data manipulation with dplyr - Applied Practice * **Objective:** Apply *r: data manipulation with dplyr* to solve concrete problems and solidify intuition. * **Theory (recap):** dplyr provides verbs (filter, select, mutate, summarize, group\_by) for expressive, chainable data manipulation. * **Practice:** Perform a group-by-summarize analysis in R using dplyr on a real dataset. ### Day 436: R: ggplot2 basics - Introduction * **Objective:** Grasp the core intuition behind *r: ggplot2 basics* before the mechanics. * **Theory:** ggplot2 builds visualizations by layering data, aesthetic mappings, and geometric objects according to the Grammar of Graphics. * **Practice:** Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences. ### Day 437: R: ggplot2 basics - Deep Dive * **Objective:** Understand the full mechanics/derivation behind *r: ggplot2 basics*. * **Theory:** ggplot2 builds visualizations by layering data, aesthetic mappings, and geometric objects according to the Grammar of Graphics. * **Practice:** Derive or re-derive the key formula/result by hand, step by step. ### Day 438: R: ggplot2 basics - Applied Practice * **Objective:** Apply *r: ggplot2 basics* to a concrete problem or dataset. * **Theory (recap):** ggplot2 builds visualizations by layering data, aesthetic mappings, and geometric objects according to the Grammar of Graphics. * **Practice:** Recreate 3 different chart types (bar, scatter, boxplot) in ggplot2 from the same dataset. ### Day 439: Python: NumPy fundamentals - Foundations * **Objective:** Build a solid conceptual understanding of *python: numpy fundamentals*. * **Theory:** NumPy provides fast array operations that underlie almost all numerical/statistical computing in Python. * **Practice:** Summarize the concept in your own words and give one real-world example before moving to application. ### Day 440: Python: NumPy fundamentals - Applied Practice * **Objective:** Apply *python: numpy fundamentals* to solve concrete problems and solidify intuition. * **Theory (recap):** NumPy provides fast array operations that underlie almost all numerical/statistical computing in Python. * **Practice:** Perform vectorized statistical computations (mean, variance, matrix ops) using NumPy without explicit loops. ### Day 441: Python: SciPy for statistics - Foundations * **Objective:** Build a solid conceptual understanding of *python: scipy for statistics*. * **Theory:** SciPy.stats provides distributions, hypothesis tests, and statistical functions built on NumPy. * **Practice:** Summarize the concept in your own words and give one real-world example before moving to application. ### Day 442: Python: SciPy for statistics - Applied Practice * **Objective:** Apply *python: scipy for statistics* to solve concrete problems and solidify intuition. * **Theory (recap):** SciPy.stats provides distributions, hypothesis tests, and statistical functions built on NumPy. * **Practice:** Run 3 different hypothesis tests using scipy.stats on a real dataset. ### Day 443: Python: Statsmodels - Introduction * **Objective:** Grasp the core intuition behind *python: statsmodels* before the mechanics. * **Theory:** Statsmodels provides classical statistical models (regression, ANOVA, time series) with detailed statistical output tables. * **Practice:** Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences. ### Day 444: Python: Statsmodels - Deep Dive * **Objective:** Understand the full mechanics/derivation behind *python: statsmodels*. * **Theory:** Statsmodels provides classical statistical models (regression, ANOVA, time series) with detailed statistical output tables. * **Practice:** Derive or re-derive the key formula/result by hand, step by step. ### Day 445: Python: Statsmodels - Applied Practice * **Objective:** Apply *python: statsmodels* to a concrete problem or dataset. * **Theory (recap):** Statsmodels provides classical statistical models (regression, ANOVA, time series) with detailed statistical output tables. * **Practice:** Fit an OLS regression in Statsmodels and interpret the full summary output table. ### Day 446: Visualization: histogram - Foundations * **Objective:** Build a solid conceptual understanding of *visualization: histogram*. * **Theory:** Histograms display the frequency distribution of a continuous variable by binning values. * **Practice:** Summarize the concept in your own words and give one real-world example before moving to application. ### Day 447: Visualization: histogram - Applied Practice * **Objective:** Apply *visualization: histogram* to solve concrete problems and solidify intuition. * **Theory (recap):** Histograms display the frequency distribution of a continuous variable by binning values. * **Practice:** Plot histograms with 3 different bin-width choices on the same dataset and compare interpretations. ### Day 448: Visualization: kernel density estimate (KDE) - Foundations * **Objective:** Build a solid conceptual understanding of *visualization: kernel density estimate (kde)*. * **Theory:** KDE smooths a histogram into a continuous estimated density curve, avoiding arbitrary binning. * **Practice:** Summarize the concept in your own words and give one real-world example before moving to application. ### Day 449: Visualization: kernel density estimate (KDE) - Applied Practice * **Objective:** Apply *visualization: kernel density estimate (kde)* to solve concrete problems and solidify intuition. * **Theory (recap):** KDE smooths a histogram into a continuous estimated density curve, avoiding arbitrary binning. * **Practice:** Overlay a KDE curve on a histogram for the same dataset and compare. ### Day 450: Visualization: QQ plot - Foundations * **Objective:** Build a solid conceptual understanding of *visualization: qq plot*. * **Theory:** A QQ plot compares sample quantiles to theoretical distribution quantiles to visually assess distributional fit (e.g. Normality). * **Practice:** Summarize the concept in your own words and give one real-world example before moving to application. ### Day 451: Visualization: QQ plot - Applied Practice * **Objective:** Apply *visualization: qq plot* to solve concrete problems and solidify intuition. * **Theory (recap):** A QQ plot compares sample quantiles to theoretical distribution quantiles to visually assess distributional fit (e.g. Normality). * **Practice:** Create QQ plots for a Normal sample and a skewed sample, and interpret the deviation pattern. ### Day 452: Visualization: box plot - Foundations * **Objective:** Build a solid conceptual understanding of *visualization: box plot*. * **Theory:** Box plots summarize the median, quartiles, and outliers of a distribution in a compact visual form. * **Practice:** Summarize the concept in your own words and give one real-world example before moving to application. ### Day 453: Visualization: box plot - Applied Practice * **Objective:** Apply *visualization: box plot* to solve concrete problems and solidify intuition. * **Theory (recap):** Box plots summarize the median, quartiles, and outliers of a distribution in a compact visual form. * **Practice:** Create side-by-side box plots comparing a variable across several categories. ### Day 454: Visualization principles for storytelling with data - Foundations * **Objective:** Build a solid conceptual understanding of *visualization principles for storytelling with data*. * **Theory:** Effective visualizations minimize clutter, choose the right chart for the data type, and highlight the intended insight clearly. * **Practice:** Summarize the concept in your own words and give one real-world example before moving to application. ### Day 455: Visualization principles for storytelling with data - Applied Practice * **Objective:** Apply *visualization principles for storytelling with data* to solve concrete problems and solidify intuition. * **Theory (recap):** Effective visualizations minimize clutter, choose the right chart for the data type, and highlight the intended insight clearly. * **Practice:** Redesign a cluttered or misleading chart into a clear, well-labeled version. ### Day 456: Practice: reproducible statistical analysis report * **Objective:** Understand and internalize *practice: reproducible statistical analysis report*. * **Theory:** A reproducible report combines code, results, and narrative so the analysis can be re-run and verified by others. * **Practice:** Produce a reproducible analysis report (e.g. R Markdown/Jupyter) with code, plots, and written interpretation. ## PHASE 10 - STATISTICS FOR MACHINE LEARNING ### Day 457: Bias-variance tradeoff - Introduction * **Objective:** Grasp the core intuition behind *bias-variance tradeoff* before the mechanics. * **Theory:** Model error decomposes into bias (systematic error from overly simple models) and variance (sensitivity to training data); minimizing total error requires balancing both. * **Practice:** Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences. ### Day 458: Bias-variance tradeoff - Deep Dive * **Objective:** Understand the full mechanics/derivation behind *bias-variance tradeoff*. * **Theory:** Model error decomposes into bias (systematic error from overly simple models) and variance (sensitivity to training data); minimizing total error requires balancing both. * **Practice:** Derive or re-derive the key formula/result by hand, step by step. ### Day 459: Bias-variance tradeoff - Applied Practice * **Objective:** Apply *bias-variance tradeoff* to a concrete problem or dataset. * **Theory (recap):** Model error decomposes into bias (systematic error from overly simple models) and variance (sensitivity to training data); minimizing total error requires balancing both. * **Practice:** Fit models of increasing complexity to the same data and plot training vs test error to visualize the tradeoff. ### Day 460: Cross-validation: k-fold - Introduction * **Objective:** Grasp the core intuition behind *cross-validation: k-fold* before the mechanics. * **Theory:** K-fold cross-validation splits data into k parts, training on k-1 and validating on the remaining part, rotating through all folds. * **Practice:** Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences. ### Day 461: Cross-validation: k-fold - Deep Dive * **Objective:** Understand the full mechanics/derivation behind *cross-validation: k-fold*. * **Theory:** K-fold cross-validation splits data into k parts, training on k-1 and validating on the remaining part, rotating through all folds. * **Practice:** Derive or re-derive the key formula/result by hand, step by step. ### Day 462: Cross-validation: k-fold - Applied Practice * **Objective:** Apply *cross-validation: k-fold* to a concrete problem or dataset. * **Theory (recap):** K-fold cross-validation splits data into k parts, training on k-1 and validating on the remaining part, rotating through all folds. * **Practice:** Implement 5-fold cross-validation manually and compare to a built-in library function. ### Day 463: Cross-validation: leave-one-out - Foundations * **Objective:** Build a solid conceptual understanding of *cross-validation: leave-one-out*. * **Theory:** Leave-one-out CV is the extreme case of k-fold where k equals the number of observations, giving low bias but high variance and cost. * **Practice:** Summarize the concept in your own words and give one real-world example before moving to application. ### Day 464: Cross-validation: leave-one-out - Applied Practice * **Objective:** Apply *cross-validation: leave-one-out* to solve concrete problems and solidify intuition. * **Theory (recap):** Leave-one-out CV is the extreme case of k-fold where k equals the number of observations, giving low bias but high variance and cost. * **Practice:** Compare leave-one-out CV and 5-fold CV results on a small dataset in terms of estimate and runtime. ### Day 465: Regularization: Ridge regression - Introduction * **Objective:** Grasp the core intuition behind *regularization: ridge regression* before the mechanics. * **Theory:** Ridge regression adds an L2 penalty on coefficients, shrinking them toward zero to reduce variance and handle multicollinearity. * **Practice:** Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences. ### Day 466: Regularization: Ridge regression - Deep Dive * **Objective:** Understand the full mechanics/derivation behind *regularization: ridge regression*. * **Theory:** Ridge regression adds an L2 penalty on coefficients, shrinking them toward zero to reduce variance and handle multicollinearity. * **Practice:** Derive or re-derive the key formula/result by hand, step by step. ### Day 467: Regularization: Ridge regression - Applied Practice * **Objective:** Apply *regularization: ridge regression* to a concrete problem or dataset. * **Theory (recap):** Ridge regression adds an L2 penalty on coefficients, shrinking them toward zero to reduce variance and handle multicollinearity. * **Practice:** Fit Ridge regression across a range of penalty values and plot the coefficient shrinkage path. ### Day 468: Regularization: Lasso regression - Foundations * **Objective:** Build a solid conceptual understanding of *regularization: lasso regression*. * **Theory:** Lasso regression adds an L1 penalty, which can shrink some coefficients exactly to zero, performing implicit feature selection. * **Practice:** Summarize the concept in your own words and give one real-world example before moving to application. ### Day 469: Regularization: Lasso regression - Applied Practice * **Objective:** Apply *regularization: lasso regression* to solve concrete problems and solidify intuition. * **Theory (recap):** Lasso regression adds an L1 penalty, which can shrink some coefficients exactly to zero, performing implicit feature selection. * **Practice:** Fit Lasso regression and identify which features are eliminated as the penalty increases. ### Day 470: Regularization: Elastic Net - Introduction * **Objective:** Grasp the core intuition behind *regularization: elastic net* before the mechanics. * **Theory:** Elastic Net combines L1 and L2 penalties, balancing Lasso's feature selection with Ridge's stability under correlated predictors. * **Practice:** Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences. ### Day 471: Regularization: Elastic Net - Deep Dive * **Objective:** Understand the full mechanics/derivation behind *regularization: elastic net*. * **Theory:** Elastic Net combines L1 and L2 penalties, balancing Lasso's feature selection with Ridge's stability under correlated predictors. * **Practice:** Derive or re-derive the key formula/result by hand, step by step. ### Day 472: Regularization: Elastic Net - Applied Practice * **Objective:** Apply *regularization: elastic net* to a concrete problem or dataset. * **Theory (recap):** Elastic Net combines L1 and L2 penalties, balancing Lasso's feature selection with Ridge's stability under correlated predictors. * **Practice:** Fit Elastic Net and compare selected features/coefficients to pure Ridge and pure Lasso. ### Day 473: Model evaluation: ROC curve - Foundations * **Objective:** Build a solid conceptual understanding of *model evaluation: roc curve*. * **Theory:** The ROC curve plots true positive rate against false positive rate across all classification thresholds. * **Practice:** Summarize the concept in your own words and give one real-world example before moving to application. ### Day 474: Model evaluation: ROC curve - Applied Practice * **Objective:** Apply *model evaluation: roc curve* to solve concrete problems and solidify intuition. * **Theory (recap):** The ROC curve plots true positive rate against false positive rate across all classification thresholds. * **Practice:** Plot an ROC curve for a binary classifier and identify a threshold matching a target false-positive rate. ### Day 475: Model evaluation: AUC - Foundations * **Objective:** Build a solid conceptual understanding of *model evaluation: auc*. * **Theory:** AUC (area under the ROC curve) summarizes classifier performance across all thresholds in a single number. * **Practice:** Summarize the concept in your own words and give one real-world example before moving to application. ### Day 476: Model evaluation: AUC - Applied Practice * **Objective:** Apply *model evaluation: auc* to solve concrete problems and solidify intuition. * **Theory (recap):** AUC (area under the ROC curve) summarizes classifier performance across all thresholds in a single number. * **Practice:** Compute AUC for two competing classifiers and determine which performs better overall. ### Day 477: Model evaluation: precision and recall - Introduction * **Objective:** Grasp the core intuition behind *model evaluation: precision and recall* before the mechanics. * **Theory:** Precision measures correctness among positive predictions; recall measures coverage of actual positives - they trade off against each other. * **Practice:** Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences. ### Day 478: Model evaluation: precision and recall - Deep Dive * **Objective:** Understand the full mechanics/derivation behind *model evaluation: precision and recall*. * **Theory:** Precision measures correctness among positive predictions; recall measures coverage of actual positives - they trade off against each other. * **Practice:** Derive or re-derive the key formula/result by hand, step by step. ### Day 479: Model evaluation: precision and recall - Applied Practice * **Objective:** Apply *model evaluation: precision and recall* to a concrete problem or dataset. * **Theory (recap):** Precision measures correctness among positive predictions; recall measures coverage of actual positives - they trade off against each other. * **Practice:** Compute precision and recall for a classifier on an imbalanced dataset and discuss the tradeoff. ### Day 480: Model evaluation: F1 score - Foundations * **Objective:** Build a solid conceptual understanding of *model evaluation: f1 score*. * **Theory:** The F1 score is the harmonic mean of precision and recall, useful as a single balanced metric especially for imbalanced classes. * **Practice:** Summarize the concept in your own words and give one real-world example before moving to application. ### Day 481: Model evaluation: F1 score - Applied Practice * **Objective:** Apply *model evaluation: f1 score* to solve concrete problems and solidify intuition. * **Theory (recap):** The F1 score is the harmonic mean of precision and recall, useful as a single balanced metric especially for imbalanced classes. * **Practice:** Compute F1 scores across different classification thresholds and find the threshold that maximizes it. ### Day 482: Bootstrap resampling - Foundations * **Objective:** Build a solid conceptual understanding of *bootstrap resampling*. * **Theory:** Bootstrap resampling repeatedly draws samples with replacement from the data to estimate the sampling distribution of a statistic. * **Practice:** Summarize the concept in your own words and give one real-world example before moving to application. ### Day 483: Bootstrap resampling - Applied Practice * **Objective:** Apply *bootstrap resampling* to solve concrete problems and solidify intuition. * **Theory (recap):** Bootstrap resampling repeatedly draws samples with replacement from the data to estimate the sampling distribution of a statistic. * **Practice:** Bootstrap a 95% confidence interval for the median of a skewed dataset. ### Day 484: Permutation tests - Foundations * **Objective:** Build a solid conceptual understanding of *permutation tests*. * **Theory:** Permutation tests assess significance by repeatedly shuffling labels to build a null distribution directly from the data. * **Practice:** Summarize the concept in your own words and give one real-world example before moving to application. ### Day 485: Permutation tests - Applied Practice * **Objective:** Apply *permutation tests* to solve concrete problems and solidify intuition. * **Theory (recap):** Permutation tests assess significance by repeatedly shuffling labels to build a null distribution directly from the data. * **Practice:** Run a permutation test to compare two group means without assuming Normality. ### Day 486: Ensemble methods: bagging - Introduction * **Objective:** Grasp the core intuition behind *ensemble methods: bagging* before the mechanics. * **Theory:** Bagging trains many models on bootstrapped samples and averages their predictions to reduce variance (e.g. Random Forest). * **Practice:** Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences. ### Day 487: Ensemble methods: bagging - Deep Dive * **Objective:** Understand the full mechanics/derivation behind *ensemble methods: bagging*. * **Theory:** Bagging trains many models on bootstrapped samples and averages their predictions to reduce variance (e.g. Random Forest). * **Practice:** Derive or re-derive the key formula/result by hand, step by step. ### Day 488: Ensemble methods: bagging - Applied Practice * **Objective:** Apply *ensemble methods: bagging* to a concrete problem or dataset. * **Theory (recap):** Bagging trains many models on bootstrapped samples and averages their predictions to reduce variance (e.g. Random Forest). * **Practice:** Train a Random Forest and compare its variance/stability to a single decision tree. ### Day 489: Ensemble methods: boosting - Foundations * **Objective:** Build a solid conceptual understanding of *ensemble methods: boosting*. * **Theory:** Boosting trains models sequentially, each correcting the errors of the previous ones, reducing bias (e.g. XGBoost). * **Practice:** Summarize the concept in your own words and give one real-world example before moving to application. ### Day 490: Ensemble methods: boosting - Applied Practice * **Objective:** Apply *ensemble methods: boosting* to solve concrete problems and solidify intuition. * **Theory (recap):** Boosting trains models sequentially, each correcting the errors of the previous ones, reducing bias (e.g. XGBoost). * **Practice:** Train a gradient boosting model and compare performance to bagging on the same dataset. ### Day 491: Information theory: entropy - Introduction * **Objective:** Grasp the core intuition behind *information theory: entropy* before the mechanics. * **Theory:** Entropy measures the average uncertainty/information content of a random variable's distribution; it underlies decision tree splitting and much of ML. * **Practice:** Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences. ### Day 492: Information theory: entropy - Deep Dive * **Objective:** Understand the full mechanics/derivation behind *information theory: entropy*. * **Theory:** Entropy measures the average uncertainty/information content of a random variable's distribution; it underlies decision tree splitting and much of ML. * **Practice:** Derive or re-derive the key formula/result by hand, step by step. ### Day 493: Information theory: entropy - Applied Practice * **Objective:** Apply *information theory: entropy* to a concrete problem or dataset. * **Theory (recap):** Entropy measures the average uncertainty/information content of a random variable's distribution; it underlies decision tree splitting and much of ML. * **Practice:** Compute the entropy of several categorical distributions by hand and confirm with code. ### Day 494: Information theory: KL divergence - Introduction * **Objective:** Grasp the core intuition behind *information theory: kl divergence* before the mechanics. * **Theory:** KL divergence measures how one probability distribution diverges from a reference distribution, central to variational inference and model comparison. * **Practice:** Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences. ### Day 495: Information theory: KL divergence - Deep Dive * **Objective:** Understand the full mechanics/derivation behind *information theory: kl divergence*. * **Theory:** KL divergence measures how one probability distribution diverges from a reference distribution, central to variational inference and model comparison. * **Practice:** Derive or re-derive the key formula/result by hand, step by step. ### Day 496: Information theory: KL divergence - Applied Practice * **Objective:** Apply *information theory: kl divergence* to a concrete problem or dataset. * **Theory (recap):** KL divergence measures how one probability distribution diverges from a reference distribution, central to variational inference and model comparison. * **Practice:** Compute KL divergence between two Normal distributions with different parameters and interpret the result. ### Day 497: Information theory: mutual information - Foundations * **Objective:** Build a solid conceptual understanding of *information theory: mutual information*. * **Theory:** Mutual information measures how much knowing one variable reduces uncertainty about another, useful for feature selection. * **Practice:** Summarize the concept in your own words and give one real-world example before moving to application. ### Day 498: Information theory: mutual information - Applied Practice * **Objective:** Apply *information theory: mutual information* to solve concrete problems and solidify intuition. * **Theory (recap):** Mutual information measures how much knowing one variable reduces uncertainty about another, useful for feature selection. * **Practice:** Compute mutual information between a feature and target variable and compare to Pearson correlation. ### Day 499: Practice: model evaluation and selection workflow * **Objective:** Understand and internalize *practice: model evaluation and selection workflow*. * **Theory:** Integrate cross-validation, regularization, and evaluation metrics into one complete model selection pipeline. * **Practice:** Build a full model selection pipeline: cross-validate several regularized models and choose the best via appropriate metrics. ## PHASE 11 - CAUSAL INFERENCE ### Day 500: Potential outcomes framework - Introduction * **Objective:** Grasp the core intuition behind *potential outcomes framework* before the mechanics. * **Theory:** The potential outcomes framework defines causal effects as the difference between an outcome under treatment and under control for the same unit, only one of which is ever observed. * **Practice:** Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences. ### Day 501: Potential outcomes framework - Deep Dive * **Objective:** Understand the full mechanics/derivation behind *potential outcomes framework*. * **Theory:** The potential outcomes framework defines causal effects as the difference between an outcome under treatment and under control for the same unit, only one of which is ever observed. * **Practice:** Derive or re-derive the key formula/result by hand, step by step. ### Day 502: Potential outcomes framework - Applied Practice * **Objective:** Apply *potential outcomes framework* to a concrete problem or dataset. * **Theory (recap):** The potential outcomes framework defines causal effects as the difference between an outcome under treatment and under control for the same unit, only one of which is ever observed. * **Practice:** Explain the 'fundamental problem of causal inference' in your own words using a concrete example. ### Day 503: Directed Acyclic Graphs (DAGs): basics - Introduction * **Objective:** Grasp the core intuition behind *directed acyclic graphs (dags): basics* before the mechanics. * **Theory:** DAGs visually encode assumed causal relationships among variables using directed edges and no cycles. * **Practice:** Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences. ### Day 504: Directed Acyclic Graphs (DAGs): basics - Deep Dive * **Objective:** Understand the full mechanics/derivation behind *directed acyclic graphs (dags): basics*. * **Theory:** DAGs visually encode assumed causal relationships among variables using directed edges and no cycles. * **Practice:** Derive or re-derive the key formula/result by hand, step by step. ### Day 505: Directed Acyclic Graphs (DAGs): basics - Applied Practice * **Objective:** Apply *directed acyclic graphs (dags): basics* to a concrete problem or dataset. * **Theory (recap):** DAGs visually encode assumed causal relationships among variables using directed edges and no cycles. * **Practice:** Draw a DAG for a real causal question you're interested in, listing all assumed relationships. ### Day 506: DAGs: confounders, mediators, colliders - Foundations * **Objective:** Build a solid conceptual understanding of *dags: confounders, mediators, colliders*. * **Theory:** Confounders bias associations if uncontrolled; mediators lie on the causal path; colliders create bias if conditioned on. * **Practice:** Summarize the concept in your own words and give one real-world example before moving to application. ### Day 507: DAGs: confounders, mediators, colliders - Applied Practice * **Objective:** Apply *dags: confounders, mediators, colliders* to solve concrete problems and solidify intuition. * **Theory (recap):** Confounders bias associations if uncontrolled; mediators lie on the causal path; colliders create bias if conditioned on. * **Practice:** Classify 5 variables in a given DAG as confounder, mediator, or collider. ### Day 508: Backdoor criterion - Introduction * **Objective:** Grasp the core intuition behind *backdoor criterion* before the mechanics. * **Theory:** The backdoor criterion identifies which variables must be controlled for to block confounding paths and isolate a causal effect. * **Practice:** Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences. ### Day 509: Backdoor criterion - Deep Dive * **Objective:** Understand the full mechanics/derivation behind *backdoor criterion*. * **Theory:** The backdoor criterion identifies which variables must be controlled for to block confounding paths and isolate a causal effect. * **Practice:** Derive or re-derive the key formula/result by hand, step by step. ### Day 510: Backdoor criterion - Applied Practice * **Objective:** Apply *backdoor criterion* to a concrete problem or dataset. * **Theory (recap):** The backdoor criterion identifies which variables must be controlled for to block confounding paths and isolate a causal effect. * **Practice:** Apply the backdoor criterion to a DAG to determine the minimal adjustment set. ### Day 511: Propensity score: concept - Foundations * **Objective:** Build a solid conceptual understanding of *propensity score: concept*. * **Theory:** The propensity score is the probability of receiving treatment given observed covariates, used to balance groups in observational data. * **Practice:** Summarize the concept in your own words and give one real-world example before moving to application. ### Day 512: Propensity score: concept - Applied Practice * **Objective:** Apply *propensity score: concept* to solve concrete problems and solidify intuition. * **Theory (recap):** The propensity score is the probability of receiving treatment given observed covariates, used to balance groups in observational data. * **Practice:** Estimate propensity scores using logistic regression on an observational dataset. ### Day 513: Propensity score matching - Introduction * **Objective:** Grasp the core intuition behind *propensity score matching* before the mechanics. * **Theory:** Propensity score matching pairs treated and control units with similar propensity scores to approximate a randomized comparison. * **Practice:** Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences. ### Day 514: Propensity score matching - Deep Dive * **Objective:** Understand the full mechanics/derivation behind *propensity score matching*. * **Theory:** Propensity score matching pairs treated and control units with similar propensity scores to approximate a randomized comparison. * **Practice:** Derive or re-derive the key formula/result by hand, step by step. ### Day 515: Propensity score matching - Applied Practice * **Objective:** Apply *propensity score matching* to a concrete problem or dataset. * **Theory (recap):** Propensity score matching pairs treated and control units with similar propensity scores to approximate a randomized comparison. * **Practice:** Perform propensity score matching and compare treatment effect estimates before and after matching. ### Day 516: Difference-in-differences - Foundations * **Objective:** Build a solid conceptual understanding of *difference-in-differences*. * **Theory:** Difference-in-differences compares the change over time between a treated and control group to estimate a causal effect, controlling for time-invariant confounders. * **Practice:** Summarize the concept in your own words and give one real-world example before moving to application. ### Day 517: Difference-in-differences - Applied Practice * **Objective:** Apply *difference-in-differences* to solve concrete problems and solidify intuition. * **Theory (recap):** Difference-in-differences compares the change over time between a treated and control group to estimate a causal effect, controlling for time-invariant confounders. * **Practice:** Estimate a treatment effect using difference-in-differences on a before/after, treatment/control dataset. ### Day 518: Instrumental variables: concept - Introduction * **Objective:** Grasp the core intuition behind *instrumental variables: concept* before the mechanics. * **Theory:** An instrumental variable affects the outcome only through its effect on the treatment, allowing causal estimation despite unobserved confounding. * **Practice:** Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences. ### Day 519: Instrumental variables: concept - Deep Dive * **Objective:** Understand the full mechanics/derivation behind *instrumental variables: concept*. * **Theory:** An instrumental variable affects the outcome only through its effect on the treatment, allowing causal estimation despite unobserved confounding. * **Practice:** Derive or re-derive the key formula/result by hand, step by step. ### Day 520: Instrumental variables: concept - Applied Practice * **Objective:** Apply *instrumental variables: concept* to a concrete problem or dataset. * **Theory (recap):** An instrumental variable affects the outcome only through its effect on the treatment, allowing causal estimation despite unobserved confounding. * **Practice:** Evaluate whether a proposed instrument satisfies relevance and exclusion restriction conditions for a given problem. ### Day 521: Instrumental variables: two-stage least squares - Foundations * **Objective:** Build a solid conceptual understanding of *instrumental variables: two-stage least squares*. * **Theory:** 2SLS first predicts treatment from the instrument, then uses predicted treatment to estimate the causal effect on the outcome. * **Practice:** Summarize the concept in your own words and give one real-world example before moving to application. ### Day 522: Instrumental variables: two-stage least squares - Applied Practice * **Objective:** Apply *instrumental variables: two-stage least squares* to solve concrete problems and solidify intuition. * **Theory (recap):** 2SLS first predicts treatment from the instrument, then uses predicted treatment to estimate the causal effect on the outcome. * **Practice:** Implement two-stage least squares by hand (two regression steps) on a simple IV dataset. ### Day 523: Regression discontinuity design - Introduction * **Objective:** Grasp the core intuition behind *regression discontinuity design* before the mechanics. * **Theory:** RDD exploits a sharp threshold rule to compare units just above and below the cutoff, approximating random assignment locally. * **Practice:** Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences. ### Day 524: Regression discontinuity design - Deep Dive * **Objective:** Understand the full mechanics/derivation behind *regression discontinuity design*. * **Theory:** RDD exploits a sharp threshold rule to compare units just above and below the cutoff, approximating random assignment locally. * **Practice:** Derive or re-derive the key formula/result by hand, step by step. ### Day 525: Regression discontinuity design - Applied Practice * **Objective:** Apply *regression discontinuity design* to a concrete problem or dataset. * **Theory (recap):** RDD exploits a sharp threshold rule to compare units just above and below the cutoff, approximating random assignment locally. * **Practice:** Design and analyze a regression discontinuity study around a policy eligibility cutoff. ### Day 526: Practice: causal inference case study * **Objective:** Understand and internalize *practice: causal inference case study*. * **Theory:** Apply the appropriate causal inference method to a realistic observational research question end-to-end. * **Practice:** Choose a causal question, select the right method (matching, DiD, IV, or RDD), and estimate the effect on real/simulated data. ## PHASE 12 - ADVANCED STATISTICS ### Day 527: Time series: autoregressive (AR) models - Foundations * **Objective:** Build a solid conceptual understanding of *time series: autoregressive (ar) models*. * **Theory:** AR models predict a value as a linear function of its own past values, capturing temporal dependence. * **Practice:** Summarize the concept in your own words and give one real-world example before moving to application. ### Day 528: Time series: autoregressive (AR) models - Applied Practice * **Objective:** Apply *time series: autoregressive (ar) models* to solve concrete problems and solidify intuition. * **Theory (recap):** AR models predict a value as a linear function of its own past values, capturing temporal dependence. * **Practice:** Fit an AR(1) model to a time series and interpret the autoregressive coefficient. ### Day 529: Time series: moving average (MA) models - Foundations * **Objective:** Build a solid conceptual understanding of *time series: moving average (ma) models*. * **Theory:** MA models predict a value as a linear function of past forecast errors rather than past values. * **Practice:** Summarize the concept in your own words and give one real-world example before moving to application. ### Day 530: Time series: moving average (MA) models - Applied Practice * **Objective:** Apply *time series: moving average (ma) models* to solve concrete problems and solidify intuition. * **Theory (recap):** MA models predict a value as a linear function of past forecast errors rather than past values. * **Practice:** Fit an MA(1) model to a time series and compare residual behavior to the AR model. ### Day 531: Time series: ARIMA - Introduction * **Objective:** Grasp the core intuition behind *time series: arima* before the mechanics. * **Theory:** ARIMA combines autoregression, differencing (for non-stationarity), and moving average components into one flexible model. * **Practice:** Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences. ### Day 532: Time series: ARIMA - Deep Dive * **Objective:** Understand the full mechanics/derivation behind *time series: arima*. * **Theory:** ARIMA combines autoregression, differencing (for non-stationarity), and moving average components into one flexible model. * **Practice:** Derive or re-derive the key formula/result by hand, step by step. ### Day 533: Time series: ARIMA - Applied Practice * **Objective:** Apply *time series: arima* to a concrete problem or dataset. * **Theory (recap):** ARIMA combines autoregression, differencing (for non-stationarity), and moving average components into one flexible model. * **Practice:** Fit an ARIMA model to a real time series after determining appropriate p, d, q orders. ### Day 534: Time series: SARIMA - Introduction * **Objective:** Grasp the core intuition behind *time series: sarima* before the mechanics. * **Theory:** SARIMA extends ARIMA with seasonal components to model recurring periodic patterns. * **Practice:** Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences. ### Day 535: Time series: SARIMA - Deep Dive * **Objective:** Understand the full mechanics/derivation behind *time series: sarima*. * **Theory:** SARIMA extends ARIMA with seasonal components to model recurring periodic patterns. * **Practice:** Derive or re-derive the key formula/result by hand, step by step. ### Day 536: Time series: SARIMA - Applied Practice * **Objective:** Apply *time series: sarima* to a concrete problem or dataset. * **Theory (recap):** SARIMA extends ARIMA with seasonal components to model recurring periodic patterns. * **Practice:** Fit a SARIMA model to seasonal data (e.g. monthly sales) and forecast the next 12 periods. ### Day 537: Time series: stationarity and unit root tests - Foundations * **Objective:** Build a solid conceptual understanding of *time series: stationarity and unit root tests*. * **Theory:** Stationarity means statistical properties don't change over time; the Augmented Dickey-Fuller test checks for a unit root (non-stationarity). * **Practice:** Summarize the concept in your own words and give one real-world example before moving to application. ### Day 538: Time series: stationarity and unit root tests - Applied Practice * **Objective:** Apply *time series: stationarity and unit root tests* to solve concrete problems and solidify intuition. * **Theory (recap):** Stationarity means statistical properties don't change over time; the Augmented Dickey-Fuller test checks for a unit root (non-stationarity). * **Practice:** Run an ADF test on a time series and, if non-stationary, apply differencing to achieve stationarity. ### Day 539: State space models - Foundations * **Objective:** Build a solid conceptual understanding of *state space models*. * **Theory:** State space models represent a time series via unobserved evolving states, estimated using tools like the Kalman filter. * **Practice:** Summarize the concept in your own words and give one real-world example before moving to application. ### Day 540: State space models - Applied Practice * **Objective:** Apply *state space models* to solve concrete problems and solidify intuition. * **Theory (recap):** State space models represent a time series via unobserved evolving states, estimated using tools like the Kalman filter. * **Practice:** Implement a simple local-level state space model and apply Kalman filtering to a noisy time series. ### Day 541: Survival analysis: Kaplan-Meier estimator - Introduction * **Objective:** Grasp the core intuition behind *survival analysis: kaplan-meier estimator* before the mechanics. * **Theory:** The Kaplan-Meier estimator non-parametrically estimates the survival function from time-to-event data, handling censoring. * **Practice:** Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences. ### Day 542: Survival analysis: Kaplan-Meier estimator - Deep Dive * **Objective:** Understand the full mechanics/derivation behind *survival analysis: kaplan-meier estimator*. * **Theory:** The Kaplan-Meier estimator non-parametrically estimates the survival function from time-to-event data, handling censoring. * **Practice:** Derive or re-derive the key formula/result by hand, step by step. ### Day 543: Survival analysis: Kaplan-Meier estimator - Applied Practice * **Objective:** Apply *survival analysis: kaplan-meier estimator* to a concrete problem or dataset. * **Theory (recap):** The Kaplan-Meier estimator non-parametrically estimates the survival function from time-to-event data, handling censoring. * **Practice:** Compute and plot a Kaplan-Meier survival curve for a censored time-to-event dataset. ### Day 544: Survival analysis: Cox proportional hazards - Introduction * **Objective:** Grasp the core intuition behind *survival analysis: cox proportional hazards* before the mechanics. * **Theory:** The Cox model estimates how covariates affect the hazard rate without specifying the baseline hazard's exact form. * **Practice:** Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences. ### Day 545: Survival analysis: Cox proportional hazards - Deep Dive * **Objective:** Understand the full mechanics/derivation behind *survival analysis: cox proportional hazards*. * **Theory:** The Cox model estimates how covariates affect the hazard rate without specifying the baseline hazard's exact form. * **Practice:** Derive or re-derive the key formula/result by hand, step by step. ### Day 546: Survival analysis: Cox proportional hazards - Applied Practice * **Objective:** Apply *survival analysis: cox proportional hazards* to a concrete problem or dataset. * **Theory (recap):** The Cox model estimates how covariates affect the hazard rate without specifying the baseline hazard's exact form. * **Practice:** Fit a Cox proportional hazards model and interpret hazard ratios for each covariate. ### Day 547: Spatial statistics: basics - Foundations * **Objective:** Build a solid conceptual understanding of *spatial statistics: basics*. * **Theory:** Spatial statistics accounts for geographic dependence, where nearby observations tend to be more similar (spatial autocorrelation). * **Practice:** Summarize the concept in your own words and give one real-world example before moving to application. ### Day 548: Spatial statistics: basics - Applied Practice * **Objective:** Apply *spatial statistics: basics* to solve concrete problems and solidify intuition. * **Theory (recap):** Spatial statistics accounts for geographic dependence, where nearby observations tend to be more similar (spatial autocorrelation). * **Practice:** Compute Moran's I to test for spatial autocorrelation in a geographic dataset. ### Day 549: Extreme value theory - Foundations * **Objective:** Build a solid conceptual understanding of *extreme value theory*. * **Theory:** Extreme value theory models the tail behavior of distributions, crucial for estimating the risk of rare, extreme events. * **Practice:** Summarize the concept in your own words and give one real-world example before moving to application. ### Day 550: Extreme value theory - Applied Practice * **Objective:** Apply *extreme value theory* to solve concrete problems and solidify intuition. * **Theory (recap):** Extreme value theory models the tail behavior of distributions, crucial for estimating the risk of rare, extreme events. * **Practice:** Fit a Generalized Extreme Value distribution to block-maxima data (e.g. annual peak river flow). ### Day 551: Stochastic processes: Markov chains - Introduction * **Objective:** Grasp the core intuition behind *stochastic processes: markov chains* before the mechanics. * **Theory:** A Markov chain's future state depends only on its current state, not its full history, described via a transition matrix. * **Practice:** Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences. ### Day 552: Stochastic processes: Markov chains - Deep Dive * **Objective:** Understand the full mechanics/derivation behind *stochastic processes: markov chains*. * **Theory:** A Markov chain's future state depends only on its current state, not its full history, described via a transition matrix. * **Practice:** Derive or re-derive the key formula/result by hand, step by step. ### Day 553: Stochastic processes: Markov chains - Applied Practice * **Objective:** Apply *stochastic processes: markov chains* to a concrete problem or dataset. * **Theory (recap):** A Markov chain's future state depends only on its current state, not its full history, described via a transition matrix. * **Practice:** Build a transition matrix for a simple Markov chain and compute its long-run stationary distribution. ### Day 554: Hidden Markov models - Introduction * **Objective:** Grasp the core intuition behind *hidden markov models* before the mechanics. * **Theory:** HMMs model systems with unobserved (hidden) states that are inferred from observed emissions, common in sequence data. * **Practice:** Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences. ### Day 555: Hidden Markov models - Deep Dive * **Objective:** Understand the full mechanics/derivation behind *hidden markov models*. * **Theory:** HMMs model systems with unobserved (hidden) states that are inferred from observed emissions, common in sequence data. * **Practice:** Derive or re-derive the key formula/result by hand, step by step. ### Day 556: Hidden Markov models - Applied Practice * **Objective:** Apply *hidden markov models* to a concrete problem or dataset. * **Theory (recap):** HMMs model systems with unobserved (hidden) states that are inferred from observed emissions, common in sequence data. * **Practice:** Implement a simple HMM and use the Viterbi algorithm to decode the most likely hidden state sequence. ### Day 557: Meta-analysis: combining study results - Foundations * **Objective:** Build a solid conceptual understanding of *meta-analysis: combining study results*. * **Theory:** Meta-analysis statistically combines effect estimates from multiple independent studies to produce a more precise overall estimate. * **Practice:** Summarize the concept in your own words and give one real-world example before moving to application. ### Day 558: Meta-analysis: combining study results - Applied Practice * **Objective:** Apply *meta-analysis: combining study results* to solve concrete problems and solidify intuition. * **Theory (recap):** Meta-analysis statistically combines effect estimates from multiple independent studies to produce a more precise overall estimate. * **Practice:** Perform a simple fixed-effects meta-analysis combining effect sizes from 3 hypothetical studies. ### Day 559: Missing data: MCAR, MAR, MNAR - Foundations * **Objective:** Build a solid conceptual understanding of *missing data: mcar, mar, mnar*. * **Theory:** Missingness mechanisms (Missing Completely At Random, At Random, Not At Random) determine which handling methods are valid. * **Practice:** Summarize the concept in your own words and give one real-world example before moving to application. ### Day 560: Missing data: MCAR, MAR, MNAR - Applied Practice * **Objective:** Apply *missing data: mcar, mar, mnar* to solve concrete problems and solidify intuition. * **Theory (recap):** Missingness mechanisms (Missing Completely At Random, At Random, Not At Random) determine which handling methods are valid. * **Practice:** Classify 3 missing-data scenarios by mechanism and justify an appropriate handling strategy for each. ### Day 561: Missing data: multiple imputation - Introduction * **Objective:** Grasp the core intuition behind *missing data: multiple imputation* before the mechanics. * **Theory:** Multiple imputation creates several plausible completed datasets, analyzes each, and pools results to properly reflect imputation uncertainty. * **Practice:** Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences. ### Day 562: Missing data: multiple imputation - Deep Dive * **Objective:** Understand the full mechanics/derivation behind *missing data: multiple imputation*. * **Theory:** Multiple imputation creates several plausible completed datasets, analyzes each, and pools results to properly reflect imputation uncertainty. * **Practice:** Derive or re-derive the key formula/result by hand, step by step. ### Day 563: Missing data: multiple imputation - Applied Practice * **Objective:** Apply *missing data: multiple imputation* to a concrete problem or dataset. * **Theory (recap):** Multiple imputation creates several plausible completed datasets, analyzes each, and pools results to properly reflect imputation uncertainty. * **Practice:** Apply multiple imputation to a dataset with missing values and compare results to simple mean imputation. ### Day 564: Statistical ethics: p-hacking and publication bias - Foundations * **Objective:** Build a solid conceptual understanding of *statistical ethics: p-hacking and publication bias*. * **Theory:** P-hacking (trying many analyses until significance appears) and publication bias (only significant results get published) distort the scientific record. * **Practice:** Summarize the concept in your own words and give one real-world example before moving to application. ### Day 565: Statistical ethics: p-hacking and publication bias - Applied Practice * **Objective:** Apply *statistical ethics: p-hacking and publication bias* to solve concrete problems and solidify intuition. * **Theory (recap):** P-hacking (trying many analyses until significance appears) and publication bias (only significant results get published) distort the scientific record. * **Practice:** Identify signs of possible p-hacking in a real or hypothetical published study. ### Day 566: Practice: capstone project - Introduction * **Objective:** Grasp the core intuition behind *practice: capstone project* before the mechanics. * **Theory:** Integrate multiple advanced topics from this phase into one substantial independent project. * **Practice:** Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences. ### Day 567: Practice: capstone project - Deep Dive * **Objective:** Understand the full mechanics/derivation behind *practice: capstone project*. * **Theory:** Integrate multiple advanced topics from this phase into one substantial independent project. * **Practice:** Derive or re-derive the key formula/result by hand, step by step. ### Day 568: Practice: capstone project - Applied Practice * **Objective:** Apply *practice: capstone project* to a concrete problem or dataset. * **Theory (recap):** Integrate multiple advanced topics from this phase into one substantial independent project. * **Practice:** Design and execute a capstone project (e.g. survival analysis or time series forecasting) on a real dataset, with a full written report.