The book *The Bayesian Choice* by Christian P. Robert is a comprehensive and advanced textbook on Bayesian Statistics. The second edition, published in 2007, builds on the first edition and includes significant updates and corrections. The book covers a wide range of topics, from the foundational aspects of Bayesian theory to advanced computational methods and applications in various fields such as medical statistics, signal processing, and finance. Key features of the book include: - **Foundational Chapters**: Chapters 1-6 provide a solid introduction to Bayesian models, decision theory, prior distributions, and Bayesian point estimation. - **Advanced Topics**: Chapters 7-9 delve into model choice, testing, and hierarchical and empirical Bayes extensions. - **Computational Methods**: Chapter 6 focuses on Markov chain Monte Carlo (MCMC) methods, including Gibbs sampling and Metropolis-Hastings algorithms. - **Model Choice**: Chapter 7 introduces methods for model selection, such as Bayes factors and reversible jump MCMC. - **Admissibility and Complete Classes**: Chapter 8 discusses admissibility conditions and complete classes of estimators. - **Invariance and Equivariant Estimators**: Chapter 9 explores invariance principles and equivariant estimators. - **Hierarchical and Empirical Bayes**: Chapter 10 covers hierarchical and empirical Bayes extensions, including their computational aspects. The book is designed for graduate students and researchers in statistics, providing a thorough understanding of Bayesian methods and their practical applications. It also includes numerous exercises and notes to enhance the reader's understanding and facilitate further study. The author, Christian P. Robert, acknowledges the contributions of many individuals who have helped improve the book, and dedicates it to his late friend José Sam Lazaro.The book *The Bayesian Choice* by Christian P. Robert is a comprehensive and advanced textbook on Bayesian Statistics. The second edition, published in 2007, builds on the first edition and includes significant updates and corrections. The book covers a wide range of topics, from the foundational aspects of Bayesian theory to advanced computational methods and applications in various fields such as medical statistics, signal processing, and finance. Key features of the book include: - **Foundational Chapters**: Chapters 1-6 provide a solid introduction to Bayesian models, decision theory, prior distributions, and Bayesian point estimation. - **Advanced Topics**: Chapters 7-9 delve into model choice, testing, and hierarchical and empirical Bayes extensions. - **Computational Methods**: Chapter 6 focuses on Markov chain Monte Carlo (MCMC) methods, including Gibbs sampling and Metropolis-Hastings algorithms. - **Model Choice**: Chapter 7 introduces methods for model selection, such as Bayes factors and reversible jump MCMC. - **Admissibility and Complete Classes**: Chapter 8 discusses admissibility conditions and complete classes of estimators. - **Invariance and Equivariant Estimators**: Chapter 9 explores invariance principles and equivariant estimators. - **Hierarchical and Empirical Bayes**: Chapter 10 covers hierarchical and empirical Bayes extensions, including their computational aspects. The book is designed for graduate students and researchers in statistics, providing a thorough understanding of Bayesian methods and their practical applications. It also includes numerous exercises and notes to enhance the reader's understanding and facilitate further study. The author, Christian P. Robert, acknowledges the contributions of many individuals who have helped improve the book, and dedicates it to his late friend José Sam Lazaro.