Mathematical Theory of Bayesian Statistics

Sumio Watanabe

April 20, 2018 Forthcoming by Chapman and Hall/CRC
Reference - 320 Pages - 50 B/W Illustrations
ISBN 9781482238068 - CAT# K23205

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Features

  • Establishes the mathematical foundation of Bayesian statistics and objectively explains Bayesian inference
  • Clarifies cases to which the conventional Bayesian laws are not applicable
  • Introduces new statistical laws which are applicable to complicated statistical models such as normal mixtures, neural networks, and hidden Markov models
  • Shows that new statistical tools such as WAIC and WBIC are useful in any circumstances

Summary

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.

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