Mathematical Theory of Bayesian StatisticsAuthor(s): Sumio Watanabe\nFormat: Paperback\nPublisher: Taylor & Francis Ltd, United Kingdom\nImprint: Chapman & Hall/CRC\nISBN-13: 9780367734817, 978-0367734817\nSynopsis\nMathematical 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. \n\nFeatures\n\nExplains Bayesian inference not subjectively but objectively. \n\nProvides a mathematical framework for conventional Bayesian theorems.\n\nIntroduces and proves new theorems. \n\nCross validation and information criteria of Bayesian statistics are studied from the mathematical point of view. \n\nIllustr.