Probability as degree of belief, updated by evidence.
9 topics · 10 curated works
No prior grounding assumed.
Statistical Rethinking 2023
Richard McElreath · 2023
Teaches Bayesian regression as choosing a generative model first and only then asking how to fit it, building intuition with simulated golems and…
Assumes you know the vocabulary.
Variational Inference: A Review for Statisticians
David M. Blei, Alp Kucukelbir & Jon D. McAuliffe · 2017
Recasts posterior approximation as an optimisation problem, trading MCMC's asymptotic guarantees for the speed needed on models MCMC cannot reach.
Primary sources and full treatments.
Bayesian Data Analysis
Gelman, Carlin, Stern, Dunson, Vehtari & Rubin · 1995
The reference for applied Bayesian work, and unusually candid about model checking and the ways a posterior can be confidently wrong.
+7 more at this level
10 works
Richard McElreath
Teaches Bayesian regression as choosing a generative model first and only then asking how to fit it, building intuition with simulated golems and globes before touching real data.
link checked 17 Sept 2026David M. Blei, Alp Kucukelbir & Jon D. McAuliffe
Recasts posterior approximation as an optimisation problem, trading MCMC's asymptotic guarantees for the speed needed on models MCMC cannot reach.
link checked 17 Sept 2026Gelman, Carlin, Stern, Dunson, Vehtari & Rubin
The reference for applied Bayesian work, and unusually candid about model checking and the ways a posterior can be confidently wrong.
link checked 17 Sept 2026Abraham Wald
Recasts estimation and hypothesis testing as decisions made under a loss function, founding statistical decision theory as a single framework covering both.
link checked 17 Sept 2026Nicholas Metropolis, Arianna W. Rosenbluth, Marshall N. Rosenbluth, Augusta H. Teller & Edward Teller
Introduces a Markov chain algorithm for sampling from a probability distribution known only up to a constant, the basis of every Metropolis-Hastings sampler since.
link checked 17 Sept 2026Thomas S. Ferguson
Constructs the Dirichlet process as a prior over probability distributions themselves, making fully nonparametric Bayesian inference possible for the first time.
link checked 17 Sept 2026Robert E. Kass & Adrian E. Raftery
Turns model comparison into a ratio of marginal likelihoods and works out how to read its magnitude as strength of evidence rather than a binary accept-or-reject decision.
link checked 17 Sept 2026Robert E. Kass & Larry Wasserman
Surveys the formal rules proposed for choosing an 'objective' prior and shows they routinely disagree with each other, so choosing a prior remains a substantive decision rather than a mechanical one.
link checked 17 Sept 2026Andrew Gelman, Xiao-Li Meng & Hal Stern
Argues a Bayesian model should be checked by comparing observed data against data simulated from its own posterior predictive distribution, not by a separate frequentist test.
link checked 17 Sept 2026Andrew Gelman
Shows the conventional inverse-gamma prior on a hierarchical variance is not actually uninformative, and proposes a half-Cauchy family that behaves better near zero.
link checked 17 Sept 2026