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Bayesian Data Analysis

by Andrew Gelman, John B. Carlin, Hal S. Stern, Donald B. Rubin · Andrew Gelman, John B. Carlin

Graduate-level reference by Gelman, Carlin, Stern, and Rubin covering Bayesian modeling from single-parameter models to hierarchical models, model checking, and computation. Readers gain the theory needed to build, fit, and criticize applied Bayesian models.

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Information Theory, Inference, and Learning Algorithms

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Doing Bayesian Data Analysis

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seeing-theory.brown.edu

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stats.stackexchange.com

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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.

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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.

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