Computational Bayesian Statistics

This textbook is structured as a general introduction to computational methods in Bayesian statistics, with a final chapter containing code samples from the most popular software packages, like BUGS and  STAN.

Theoretical notions are introduced as needed. After a general, ‘philosophical’ first chapter on the comparison between the inferential and the Bayesian paradigm, Chapter 2 gives an overview of the basic approaches to represent prior information, for example, Jeffrey’s prior and the conjugate priors. Markov Chain - Monte Carlo (MCMC) methods, one of the pillars of the field, are explained in chapter 6. However, the presentation is intended as a quick summary, or review, without proofs, and the reader seeking a thorough theoretical understanding should clearly complement the reading with other books. 

An alternative to MCMC is the use of analytic approximations, reviewed in chapter 8. The authors introduce the integrated and nested Laplace approximations (INLA), a relatively recent technique that allows fast and deterministic approximation of marginal posterior distributions. This is, in my opinion, the most interesting chapter, given that INLA are not frequently included in introductory books on Bayesian data analysis.

The authors provide numerous examples, figures, and exercises (but no solutions or hints) throughout the book. I strongly recommend to try out the problems, especially those involving some hands-on practical simulation.

I think this book can be seen as a short guided tour through a vast landscape. It is readable by anyone with a general background in statistics and would be appropriate for a short course (in fact, it is based on lecture notes from a short course that was given at the XXII Congress of the Portuguese Statistical Society.)

Fabio Mainardi (fabio.mainardi@rd.nestle.com) is a mathematician working as a senior data scientist at Nestlé Research. His mathematical interests are number theory, functional analysis, discrete mathematics and probability.