Mathematical Theory of Bayesian Statistics

by Sumio Watanabe

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

Genres: Mathematics

320 pages, Hardcover

Published April 23, 2018

Reviews

[Christian ROBERT · Rating 3 out of 5]

This book exposes in detail a specific perspective on Bayesian analysis, namely the use of information criteria in Bayesian statistics and in particular in Bayesian model comparison, through the Widely Applicable Information Criterion (WAIC) introduced by the author in 2013. The result is a very technical book with little motivation or intuition surrounding the mathematical results. Some background on mathematical statistics and Bayesian inference is preferable and the book cannot be used as a textbook for most audiences, as opposed to eg An Introduction to Bayesian Analysis by J.K. Ghosh et al. or Principles of Uncertainty by J. Kadane.