'The authors of Computational Bayesian Statistics very wisely draw a line in the sand around the software and methodology associated with more traditional Bayesian statistical inference. The slender volume swiftly establishes Bayesian fundamentals, covers most of the more established and time?proven inference methods, and eventually concludes with its unique selling point: a comprehensive treatment of various software packages, chiefly BUGS, JAGS, STAN, BayesX, and R?INLA. … In this sense, the book acts as a powerful springboard for students to dive into the mighty deluge of Bayesian computational methods from our present-day position on the riverbank.' Biometrical Journal

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.

1. Bayesian inference
2. Representation of prior information
3. Bayesian inference in basic problems
4. Inference by Monte Carlo methods
5. Model assessment
6. Markov chain Monte Carlo methods
7. Model selection and transdimensional MCMC
8. Methods based on analytic approximations
9. Software.

Subject Areas: Machine learning [UYQM], Probability & statistics [PBT], Economic statistics [KCHS], Data analysis: general [GPH]