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OverviewMathematical 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. Full Product DetailsAuthor: Sumio WatanabePublisher: Taylor & Francis Ltd Imprint: Chapman & Hall/CRC Weight: 0.280kg ISBN: 9780367734817ISBN 10: 0367734818 Pages: 332 Publication Date: 18 December 2020 Audience: College/higher education , General/trade , Tertiary & Higher Education , General Format: Paperback Publisher's Status: Active Availability: In Print This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. Table of ContentsReviewsInformation criteria are introduced from the two viewpoints, model selection and hyperparameter optimization. In each viewpoint, the properties of the generalization loss and the free energy or the minus log marginal likelihood are investigated. The book is very nicely written with well-defined concepts and contexts. I recommend to all students and researchers. ~Rozsa Horvath-Bokor, Zentralblatt MATH Information criteria are introduced from the two viewpoints, model selection and hyperparameter optimization. In each viewpoint, the properties of the generalization loss and the free energy or the minus log marginal likelihood are investigated. The book is very nicely written with well-defined concepts and contexts. I recommend to all students and researchers. Rozsa Horvath-Bokor, Zentralblatt MATH Author InformationSumio Watanabe is a professor in the Department of Computational Intelligence and Systems Science at Tokyo Institute of Technology, Japan. Tab Content 6Author Website:Countries AvailableAll regions |