Computational Bayesian Statistics

Maria 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 Centre 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 & Data Science at the University of Texas at Austin. He has published widely on computational methods in Bayesian statistics, nonparametric 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, nonparametric Bayesian inference, medical decision making, and more.

'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

• 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.