Mathematical Theory of Bayesian Statistics

Nonfiction, Science & Nature, Mathematics, Statistics
Cover of the book Mathematical Theory of Bayesian Statistics by Sumio Watanabe, CRC Press
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Author: Sumio Watanabe ISBN: 9781315355696
Publisher: CRC Press Publication: April 27, 2018
Imprint: Chapman and Hall/CRC Language: English
Author: Sumio Watanabe
ISBN: 9781315355696
Publisher: CRC Press
Publication: April 27, 2018
Imprint: Chapman and Hall/CRC
Language: English

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 ScienceĀ at Tokyo Institute of Technology. He studies the relationship between algebraic geometry and mathematical statistics.

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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

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 ScienceĀ at Tokyo Institute of Technology. He studies the relationship between algebraic geometry and mathematical statistics.

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