The Annals of Applied Statistics

Bayesian inference and the parametric bootstrap

Bradley Efron

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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.

Article information

Source
Ann. Appl. Stat., Volume 6, Number 4 (2012), 1971-1997.

Dates
First available in Project Euclid: 27 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.aoas/1356629067

Digital Object Identifier
doi:10.1214/12-AOAS571

Mathematical Reviews number (MathSciNet)
MR3058690

Zentralblatt MATH identifier
1257.62027

Keywords
Jeffreys prior exponential families deviance generalized linear models

Citation

Efron, Bradley. Bayesian inference and the parametric bootstrap. Ann. Appl. Stat. 6 (2012), no. 4, 1971--1997. doi:10.1214/12-AOAS571. https://projecteuclid.org/euclid.aoas/1356629067


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