formalStatistics
The probability and statistics foundations behind modern machine learning.
Deep-dive explainers combining rigorous mathematics, interactive visualizations, and working code. The bridge between formalCalculus and formalML.
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Sample Spaces, Events & Axioms
The Kolmogorov axioms, sigma-algebras, combinatorial probability, and the union bound that powers PAC learning.
9 Tracks · 32 Topics · 3 planned
Foundations of Probability
Kolmogorov axioms, conditional probability, random variables, expectation
Core Distributions & Families
Discrete and continuous distributions, exponential families, multivariate distributions
Convergence & Limit Theorems
Modes of convergence, law of large numbers, central limit theorem, tail bounds
Statistical Estimation
Bias-variance, maximum likelihood, method of moments, sufficiency
Hypothesis Testing & Confidence
Neyman-Pearson paradigm, likelihood ratio tests, confidence intervals, multiple testing
Regression & Linear Models
Least squares, generalized linear models, regularization, model selection
Bayesian Statistics
Prior selection, MCMC computation, model comparison, hierarchical models
High-Dimensional & Nonparametric
Order statistics, kernel density estimation, bootstrap, empirical processes
Time-Series & State-Space Methods
Hidden Markov models, state-space inference, and the foundations of time-series statistics
Prerequisite Graph
The full dependency graph — arrows show prerequisites. Click any node to open the topic.