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Mathematical Theory of Bayesian Statistics

Sumio Watanabe
€229.40
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A01=Sumio Watanabe
advanced probability concepts
algebraic geometry applications
Author_Sumio Watanabe
Bayesian Hypothesis Test
Bayesian Lasso
Category=PBTB
Cross Validation
Cross Validation Error
density
Detailed Balance Condition
Dirichlet Process
distribution
energy
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
error
free
generalization
Generalization Error
Generalization Loss
Gibbs Sampler
Hierarchical Bayesian Estimation
Hyperparameter Optimization
hypothesis testing framework
Kullback Leibler Distance
loss
Markov Chain Monte Carlo Method
MCMC Algorithm
MCMC Process
Metropolis Method
model selection techniques
Nonparametric Bayesian
Normal Mixture
objective Bayesian inference for researchers
Parallel Tempering
posterior
Posterior Distribution
predictive analytics methods
Predictive Density
probability
Resolution Theorem
statistical learning theory
true
True Conditional Density
True Distribution
True Statistical Model

Product details

  • ISBN 9781482238068
  • Weight: 770g
  • Dimensions: 156 x 234mm
  • Publication Date: 23 Apr 2018
  • Publisher: Taylor & Francis Inc
  • Publication City/Country: US
  • Product Form: Hardback
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Description

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.

About Sumio Watanabe

Sumio Watanabe is a professor in the Department of Computational Intelligence and Systems Science at Tokyo Institute of Technology, Japan.

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