Computational Bayesian statistics: an introduction/ Maria Antonia Amaral Turkman, Carlos Daniel Paulino, Peter Muller

Includes bibliography and index

Bayesian inference -- Representation of prior information -- Bayesian inference in basic problems -- Inference by Monte Carlo Methods -- Model assessment -- Markov Chain Monte Carlo methods -- Model selection and trans-dimensional MCMC -- Methods based on analytic approximations -- Software

Meaningful use of advanced Bayesian methods requires a good understanding of the fundamentals. This engaging book explains the ideas that underpin the construction and analysis of Bayesian models, with particular focus on computational methods and schemes. The unique features of the text are the extensive discussion of available software packages combined with a brief but complete and mathematically rigorous introduction to Bayesian inference. The text introduces Monte Carlo methods, Markov chain Monte Carlo methods, and Bayesian software, with additional material on model validation and comparison, transdimensional MCMC, and conditionally Gaussian models. The inclusion of problems makes the book suitable as a textbook for a first graduate-level course in Bayesian computation with a focus on Monte Carlo methods. The extensive discussion of Bayesian software - R/R-INLA, OpenBUGS, JAGS, STAN, and BayesX - makes it useful also for researchers and graduate students from beyond statistics.