TY - BOOK
AU - Watanabe, Sumio
TI - Mathematical theory of bayesian statistics
SN - 9781482238068
U1 - 519.5â42
PY - 2018///
CY - New York
PB - CRC Press
KW - Mathematics
KW - Statistics
KW - Mathematical models
KW - Bayesian statistical decision theory
N2 - 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.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, hyper parameter optimization, and hypothesis tests.This book provides basic introductions for students, researchers, and users of Bayesian statistics, as well as applied mathematicians.
https://www.crcpress.com/Mathematical-Theory-of-Bayesian-Statistics/Watanabe/p/book/9781482238068
ER -