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Bayesian inference and the parametric bootstrap. (English) Zbl 1257.62027

Summary: 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.

MSC:

62F15 Bayesian inference
62F40 Bootstrap, jackknife and other resampling methods
62J12 Generalized linear models (logistic models)
65C60 Computational problems in statistics (MSC2010)

Software:

bootstrap
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References:

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