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December 2012 Bayesian inference and the parametric bootstrap
Bradley Efron
Ann. Appl. Stat. 6(4): 1971-1997 (December 2012). DOI: 10.1214/12-AOAS571

Abstract

The parametric bootstrap can be used for the efficient computation of Bayes posterior distributions. Importance sampling formulas take on an easy form relating to the deviance in exponential families and are particularly simple starting from Jeffreys invariant prior. Because of the i.i.d. nature of bootstrap sampling, familiar formulas describe the computational accuracy of the Bayes estimates. Besides computational methods, the theory provides a connection between Bayesian and frequentist analysis. Efficient algorithms for the frequentist accuracy of Bayesian inferences are developed and demonstrated in a model selection example.

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Bradley Efron. "Bayesian inference and the parametric bootstrap." Ann. Appl. Stat. 6 (4) 1971 - 1997, December 2012. https://doi.org/10.1214/12-AOAS571

Information

Published: December 2012
First available in Project Euclid: 27 December 2012

zbMATH: 1257.62027
MathSciNet: MR3058690
Digital Object Identifier: 10.1214/12-AOAS571

Keywords: deviance , exponential families , generalized linear models , Jeffreys prior

Rights: Copyright © 2012 Institute of Mathematical Statistics

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Vol.6 • No. 4 • December 2012
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