Mathematical Theory of Bayesian Statistics

Sumio Watanabe

2018년 4월 · CRC Press

eBook

330

페이지

적용 가능

검증되지 않은 평점과 리뷰입니다. 자세히 알아보기

eBook 정보

Mathematical Theory of Bayesian Statistics introduces the mathematical foundation of Bayesian inference which is well-known to be more accurate in many real-world problems than the maximum likelihood method. Recent research has uncovered several mathematical laws in Bayesian statistics, by which both the generalization loss and the marginal likelihood are estimated even if the posterior distribution cannot be approximated by any normal distribution.

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.