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Mathematical Theory of Bayesian Statistics

Mathematical Theory of Bayesian Statistics

by Sumio Watanabe
Hardback
Publication Date: 08/05/2018

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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

  • 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.

ISBN:
9781482238068
9781482238068
Category:
Psychological methodology
Format:
Hardback
Publication Date:
08-05-2018
Language:
English
Publisher:
CRC Press LLC
Country of origin:
United States
Dimensions (mm):
242x162x26mm
Weight:
0.77kg

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