Mathematical Theory of Bayesian Statistics
Auteur : Watanabe Sumio
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.
Mathematical Theory of Bayesian Statistics
Sumio Watanabe is a professor in the Department of Computational Intelligence and Systems Science at Tokyo Institute of Technology, Japan.
Date de parution : 12-2020
15.6x23.4 cm
Date de parution : 04-2018
15.6x23.4 cm
Thèmes de Mathematical Theory of Bayesian Statistics :
Mots-clés :
Posterior Distribution; Generalization Loss; posterior; Generalization Error; distribution; True Distribution; free; Kullback Leibler Distance; energy; Cross Validation Error; generalization; Hyperparameter Optimization; loss; Normal Mixture; error; Gibbs Sampler; true; Nonparametric Bayesian; probability; Markov Chain Monte Carlo Method; density; True Conditional Density; Predictive Density; Cross Validation; True Statistical Model; Hierarchical Bayesian Estimation; Detailed Balance Condition; Bayesian Lasso; MCMC Process; Dirichlet Process; Bayesian Hypothesis Test; Metropolis Method; Resolution Theorem; MCMC Algorithm; Parallel Tempering