A self-contained introduction to probability, exchangeability and Bayes’ rule provides a theoretical understanding of the applied material. Numerous examples with R-code that can be run "as-is" allow the reader to perform the data analyses themselves. The development of Monte Carlo and Markov chain Monte Carlo methods in the context of data analysis examples provides motivation for these computational methods.
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Andrew Gelman, John B. Carlin, Hal S. Stern, David B. Dunson, Aki Vehtari, Donald B. Rubin. Murray, J. S., Dunson, D. B., Carin, L., and Lucas, J. E. (2013). ... Neal, R. M. (1993). Probabilistic inference using Markov chain Monte Carlo ...
This book focuses on Bayesian methods applied routinely in practice including multiple linear regression, mixed effects models and generalized linear models (GLM).
Supported by a wealth of learning features, exercises, and visual elements as well as online video tutorials and interactive simulations, this book is the first student-focused introduction to Bayesian statistics.
Gelfand, A. E., Sahu, S. K., and Carlin, B. P. (1995). Efficient parameterisations for normal linear mixed models. Biometrika, (82):479–488. Gelman, A. (2005). Analysis of variance: Why it is moreimportant than ever.
This book provides basic introductions for students, researchers, and users of Bayesian statistics, as well as applied mathematicians.
"...this edition is useful and effective in teaching Bayesian inference at both elementary and intermediate levels.
The book consists of 12 chapters, starting with basic concepts and covering numerous topics, including Bayesian estimation, decision theory, prediction, hypothesis testing, hierarchical models, Markov chain Monte Carlo methods, finite ...
This is an introduction to Bayesian statistics and decision theory, including advanced topics such as Monte Carlo methods. This new edition contains several revised chapters and a new chapter on model choice.
The prerequisites for the book are a basic knowledge of probability theory and of statistics. Methodological and data-based exercises are included within the main text and students are expected to solve them as they read the book.