Mathematical Theory of Bayesian Statistics

Features

• Explains Bayesian inference not subjectively but objectively.
• Provides a mathematical framework for conventional Bayesian theorems.
• Introduces and proves new theorems.
• Cross validation and information criteria of Bayesian statistics are studied from the mathematical point of view.
• Illustrates applications to several statistical problems, for example, model selection, hyperparameter optimization, and hypothesis tests.

This book provides basic introductions for students, researchers, and users of Bayesian statistics, as well as applied mathematicians.

Author

Sumio Watanabe is a professor of Department of Mathematical and Computing Science at Tokyo Institute of Technology. He studies the relationship between algebraic geometry and mathematical statistics.