Bayes for beginners



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 about getting into it. No attempt is made to be comprehensive, novel, or to even expert.

Workflow

Everyone references Bayesian Data Analysis (free online, with copious learning notes) as a first stopping point. 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.

See also BAT the Bayesian Analysis Toolkit, which does sophisticated Bayes modelling although AFAICT uses a fairly basic Sampler?

Notes on Rao-Blackwellisation for doing faster MCMC inference, and even handling discrete parameters in Stan.

Nonparametrics

Dirichlet processes, Gaussian Process regression etc. πŸ—

References

Alquier, Pierre. 2021. β€œUser-Friendly Introduction to PAC-Bayes Bounds.” arXiv:2110.11216 [Cs, Math, Stat], October.
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Barbier, Jean, and Nicolas Macris. 2017. β€œThe Stochastic Interpolation Method: A Simple Scheme to Prove Replica Formulas in Bayesian Inference.” arXiv:1705.02780 [Cond-Mat], May.
Bernardo, JosΓ© 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. β€œThe Stan Math Library: Reverse-Mode Automatic Differentiation in C++.” arXiv Preprint arXiv:1509.07164.
Caruana, Rich. 1998. β€œMultitask Learning.” In Learning to Learn, 95–133. Springer, Boston, MA.
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Gabry, Jonah, Daniel Simpson, Aki Vehtari, Michael Betancourt, and Andrew Gelman. 2019. β€œVisualization in Bayesian Workflow.” Journal of the Royal Statistical Society: Series A (Statistics in Society) 182 (2): 389–402.
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