Annals of Applied Statistics

Bayesian inference and the parametric bootstrap

Bradley Efron

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

First available in Project Euclid: 27 December 2012

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Jeffreys prior exponential families deviance generalized linear models


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

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