Not covered: controversy, about legitimacy of Bayesian statistics, or how often this tool is overegged and used as a philosophy of science itself.
Even for the most currmudgeonly frequentist it is sometimes refreshing to move your effort from deriving frequentist estimators for intractable models, to using the damn Bayesian ones, which fail in different and interesting ways than you are used to. If it works and you are feeling fancy you might then justify your Bayesian method on frequentist grounds, which washes away the sin.
Here are some scattered tidbits here about getting into it. Not attempt is made to be comprehensive, novel, or to even expert.
Is weird and important. Here are some argumentative and disputed rules of thumb.
Everyone references Bayesian Data Analysis as a first stopping point here. It is simple and readable.
The visualisation howto from, basically, the Stan team, is a deeper than it sounds. (Gabry et al. 2019)
Michael Betancourt’s examples, for example his workflow tips, are a good start.
Chris Fonnesbeck’s workshop in R.
Intro to Stan for econometrics.
Dirichlet processes, Gaussian Processes etc. 🚧
See probabilistic programming.
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Barbier, Jean, and Nicolas Macris. 2017. “The Stochastic Interpolation Method: A Simple Scheme to Prove Replica Formulas in Bayesian Inference,” May. http://arxiv.org/abs/1705.02780.
Bernardo, José M., and Adrian F. M. Smith. 2000. Bayesian Theory. 1 edition. Chichester: Wiley.
Carpenter, Bob, Matthew D. Hoffman, Marcus Brubaker, Daniel Lee, Peter Li, and Michael Betancourt. 2015. “The Stan Math Library: Reverse-Mode Automatic Differentiation in C++.” arXiv Preprint arXiv:1509.07164. http://arxiv.org/abs/1509.07164.
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Gabry, Jonah, Daniel Simpson, Aki Vehtari, Michael Betancourt, and Andrew Gelman. 2019. “Visualization in Bayesian Workflow.” Journal of the Royal Statistical Society: Series A (Statistics in Society) 182 (2): 389–402. https://doi.org/10.1111/rssa.12378.
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Gelman, Andrew, John B. Carlin, Hal S. Stern, David B. Dunson, Aki Vehtari, and Donald B. Rubin. 2013. Bayesian Data Analysis. 3 edition. Boca Raton: Chapman and Hall/CRC.
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Li, Meng, and David B. Dunson. 2016. “A Framework for Probabilistic Inferences from Imperfect Models,” November. http://arxiv.org/abs/1611.01241.
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