The book "The Bayesian Choice" by Christian P. Robert is a comprehensive resource on Bayesian statistics, covering both theoretical foundations and practical applications. The second edition, published in 2007, includes updates and corrections from the first edition, which was based on a French version. The book emphasizes the Bayesian approach, providing a detailed exploration of decision-theoretic foundations and computational methods. Key features of the book include: - **Decision-Theoretic Foundations**: The book starts with an introduction to statistical models and the Bayesian paradigm, followed by a thorough discussion of decision theory, including minimaxity and admissibility. - **Bayesian Point Estimation**: It covers Bayesian inference, decision theory, sampling models, and dynamic models, with a focus on normal models and linear regression. - **Tests and Confidence Regions**: The book discusses classical and Bayesian approaches to testing and confidence regions, including the Bayes factor and posterior probabilities. - **Bayesian Calculations**: It delves into classical approximation methods and Markov chain Monte Carlo (MCMC) methods, providing practical insights into Bayesian computations. - **Model Choice**: A new chapter on model choice is introduced, covering standard frameworks, Monte Carlo and MCMC approximations, model averaging, and goodness-of-fit. - **Admissibility and Complete Classes**: The book explores admissibility conditions, complete classes, and necessary conditions for admissibility. - **Invariance, Haar Measures, and Equivariant Estimators**: It discusses invariance principles, equivariant estimators, and the Hunt–Stein theorem. - **Hierarchical and Empirical Bayes Extensions**: The book examines hierarchical and empirical Bayes extensions, including optimality of hierarchical Bayes estimators and justifications for the empirical Bayes approach. The book is designed for graduate students and researchers in statistics, providing a broad and deep understanding of Bayesian statistics, from theoretical foundations to practical implementation. It includes numerous exercises and notes to enhance understanding and encourage further exploration.The book "The Bayesian Choice" by Christian P. Robert is a comprehensive resource on Bayesian statistics, covering both theoretical foundations and practical applications. The second edition, published in 2007, includes updates and corrections from the first edition, which was based on a French version. The book emphasizes the Bayesian approach, providing a detailed exploration of decision-theoretic foundations and computational methods. Key features of the book include: - **Decision-Theoretic Foundations**: The book starts with an introduction to statistical models and the Bayesian paradigm, followed by a thorough discussion of decision theory, including minimaxity and admissibility. - **Bayesian Point Estimation**: It covers Bayesian inference, decision theory, sampling models, and dynamic models, with a focus on normal models and linear regression. - **Tests and Confidence Regions**: The book discusses classical and Bayesian approaches to testing and confidence regions, including the Bayes factor and posterior probabilities. - **Bayesian Calculations**: It delves into classical approximation methods and Markov chain Monte Carlo (MCMC) methods, providing practical insights into Bayesian computations. - **Model Choice**: A new chapter on model choice is introduced, covering standard frameworks, Monte Carlo and MCMC approximations, model averaging, and goodness-of-fit. - **Admissibility and Complete Classes**: The book explores admissibility conditions, complete classes, and necessary conditions for admissibility. - **Invariance, Haar Measures, and Equivariant Estimators**: It discusses invariance principles, equivariant estimators, and the Hunt–Stein theorem. - **Hierarchical and Empirical Bayes Extensions**: The book examines hierarchical and empirical Bayes extensions, including optimality of hierarchical Bayes estimators and justifications for the empirical Bayes approach. The book is designed for graduate students and researchers in statistics, providing a broad and deep understanding of Bayesian statistics, from theoretical foundations to practical implementation. It includes numerous exercises and notes to enhance understanding and encourage further exploration.