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This graduate-level textbook presents an introduction to Bayesian statistics and decision theory. Its scope covers both the basic ideas of statistical theory, but also some of the more modern and advanced topics of Bayesian statistics such as complete class theorems, Stein effects, hierarchical and empirical modelling, and Gibbs sampling. It is the translation of a successful French text. In the translation to the English edition, the author has taken the opportunity to add and update material, and to include many problems and exercises for students. From reviews of the French edition: "I strongly encourage everyone teaching Bayesian decision theory to use (this) as the main textbook." Journal of the American Statistical Association