Bayes Rules!
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Free online textbook by Johnson, Ott, and Dogucu covering Bayes' rule, conjugate families, MCMC simulation, and hierarchical regression models. Exercises use R with rstan and rstanarm, so readers finish able to fit and check Bayesian models.
More resources on Bayesian Statistics
Information Theory, Inference, and Learning Algorithms
David MacKay's textbook, free to read online, covering entropy, data compression, noisy-channel coding, error-correcting codes, Bayesian inference, Monte Carlo methods and neural networks. Readers come to understand Shannon's coding theorems and apply probabilistic reasoning to communication and learning problems.
Doing Bayesian Data Analysis
Kruschke teaches Bayesian inference step by step with worked R and JAGS code, moving from probability basics to hierarchical models and Bayesian analogues of t-tests, ANOVA, and regression. Assumes only introductory statistics.
seeing-theory.brown.edu
Seeing Theory is an interactive, browser-based resource from Brown University that uses visual simulations to explain fundamental probability and statistics concepts. It offers interactive demos and explanations on topics like probability, distributions, sampling, the central limit theorem, confidence intervals, hypothesis testing, and Bayesian reasoning.
stats.stackexchange.com
Stats Stack Exchange is a Q&A community for statistics professionals and enthusiasts, featuring questions and expert answers on topics from probability and inference to data analysis and experimental design. It’s a practical resource for learning statistical concepts, getting help with methods, and discussing real-world data problems.
PyMC Documentation
Official documentation for PyMC, the Python library for probabilistic programming, with installation guides, API reference, and worked example notebooks. Covers specifying priors and likelihoods, running MCMC samplers, and checking posterior results.
Think Bayes 2e
Allen Downey's free online textbook teaches Bayesian statistics computationally in Python, with every chapter as a runnable Jupyter notebook. Covers distributions, MCMC, regression, and survival analysis, using code and simulation instead of heavy calculus.