Topics
32 topics across 8 tracks — published topics are linked, the rest are coming soon.
Foundations of Probability
Kolmogorov axioms, conditional probability, random variables, expectation
Conditional Probability & Independence
Bayes' theorem, law of total probability, independence
Random Variables & Distributions
Measurable functions, PMFs and PDFs, CDFs
Expectation, Variance & Moments
Integration against a measure, moment-generating functions
Core Distributions & Families
Discrete and continuous distributions, exponential families, multivariate distributions
Discrete Distributions
Bernoulli, Binomial, Poisson, Geometric
Continuous Distributions
Normal, Exponential, Gamma, Beta, Uniform
Exponential Families
Sufficient statistics, natural parameters
Multivariate Distributions
Joint, marginal, conditional densities
Convergence & Limit Theorems
Modes of convergence, law of large numbers, central limit theorem, tail bounds
Modes of Convergence
Almost sure, in probability, in distribution, in Lp
Law of Large Numbers
Weak and strong LLN
Central Limit Theorem
Lindeberg-Lévy, Berry-Esseen bound
Large Deviations & Tail Bounds
Markov, Chebyshev, Chernoff, Hoeffding bounds
Statistical Estimation
Bias-variance, maximum likelihood, method of moments, sufficiency
Point Estimation & Bias-Variance
Bias-variance, MSE decomposition
Maximum Likelihood Estimation
Likelihood function, Fisher information
Method of Moments & M-Estimation
Moment equations, M-estimation
Sufficient Statistics & Rao-Blackwell
UMVUE, Rao-Blackwell, completeness
Hypothesis Testing & Confidence
Neyman-Pearson paradigm, likelihood ratio tests, confidence intervals, multiple testing
Hypothesis Testing Framework
Type I/II errors, power, p-values
Likelihood Ratio Tests & Neyman-Pearson
Neyman-Pearson lemma, Wilks' theorem
Confidence Intervals & Duality
Pivotal quantities, coverage probability
Multiple Testing & False Discovery
Bonferroni, Benjamini-Hochberg FDR
Regression & Linear Models
Least squares, generalized linear models, regularization, model selection
Simple & Multiple Linear Regression
Least squares, Gauss-Markov theorem
Generalized Linear Models
Link functions, deviance
Regularization & Penalized Estimation
Ridge, lasso, elastic net
Model Selection & Information Criteria
AIC, BIC, cross-validation theory
Bayesian Statistics
Prior selection, MCMC computation, model comparison, hierarchical models
Bayesian Foundations & Prior Selection
Prior selection, conjugacy, Jeffreys priors
Bayesian Computation
MCMC, Metropolis-Hastings, Gibbs sampling
Bayesian Model Comparison
Bayes factors, marginal likelihood
Hierarchical & Empirical Bayes
Multilevel models, shrinkage estimators
High-Dimensional & Nonparametric
Order statistics, kernel density estimation, bootstrap, empirical processes
Order Statistics & Quantiles
Quantile asymptotics, distribution-free inference
Kernel Density Estimation
Bandwidth selection, bias-variance
The Bootstrap
Efron's bootstrap, bootstrap confidence intervals
Empirical Processes & Uniform Convergence
Glivenko-Cantelli, Donsker, VC dimension