Computational Bayesian Statistics: An Introduction(Series Number 11 Institute of Mathematical Statistics Textbooks)

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.

Table of Contents:
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.

About the Author :
M. Antónia Amaral Turkman was, until 2013, full-time Professor in the Department of Statistics and Operations Research, Faculty of Sciences, University of Lisbon. Though retired from the university, she is still a member of its Center of Statistics and Applications, where she held the position of scientific coordinator until 2017. Her research interests are Bayesian statistics, medical and environmental statistics, and spatiotemporal modeling, with recent publications on computational methods in Bayesian statistics, with an emphasis on applications in health and forest fires. She has served as vice president of the Portuguese Statistical Society. She has taught courses on Bayesian statistics and computational statistics, among many others. Carlos Daniel Paulino is senior academic researcher in the Center of Statistics and Applications and was associate professor with habilitation in the Department of Mathematics of the Instituto Superior Técnico, both at the University of Lisbon. He has published frequently on Bayesian statistics and categorical data, with emphasis on applications in biostatistics. He has served as president of the Portuguese Statistical Society. He taught many undergraduate and graduate level courses, notably in mathematical statistics and Bayesian statistics. Peter Müller is Professor in the Department of Mathematics and the Department of Statistics and Data Science at the University of Texas, Austin. He has published widely on computational methods in Bayesian statistics, non-parametric Bayesian statistics, and decision problems, with emphasis on applications in biostatistics and bioinformatics. He has served as president of the International Society for Bayesian Analysis, and as chair for the Section on Bayesian Statistics of the American Statistical Association. Besides many graduate-level courses he has taught short courses on Bayesian biostatistics, Bayesian clinical trial design, non-parametric Bayesian inference, medical decision making, and more.

Review :
'An introduction to computational Bayesian statistics cooked to perfection, with the right mix of ingredients, from the spirited defense of the Bayesian approach, to the description of the tools of the Bayesian trade, to a definitely broad and very much up-to-date presentation of Monte Carlo and Laplace approximation methods, to a helpful description of the most common software. And spiced up with critical perspectives on some common practices and a healthy focus on model assessment and model selection. Highly recommended on the menu of Bayesian textbooks!' Christian Robert, Université de Paris IX, Paris-Dauphine, and University of Warwick 'This book aims to be a concise introduction to modern computational Bayesian statistics, and it certainly succeeds! The authors carefully introduce every main technique that is around and demonstrate its use with the appropriate software. Additionally, the book contains a readable introduction to Bayesian methods, and brings the reader up to speed within the field in no time!' Håvard Rue, King Abdullah University of Science and Technology, Saudi Arabia 'Exercises are presented at the end of each chapter, with just over sixty such exercises in total - enough to provide some exposure to the practical problems which arise without being overwhelming. Overall the book is approachable and clearly written and numerous examples clarify abstract ideas as they arise.' Adam M. Johansen, Mathematical Reviews Clippings '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