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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