Mathematical Theory of Bayesian Statistics

This book introduces the mathematical foundation of Bayesian statistics. It is well known that Bayesian inference is more accurate than the maximum likelihood method in many real-world problems: however, its mathematical foundations have been left unexplained. Recently, new research on Bayesian statistics uncovered the mathematical laws by which the behavior of Bayesian inference can be estimated and the advances of Bayes estimation have been clarified. This book introduces such mathematical foundations to students and researchers.