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October 2011 Computational approaches for empirical Bayes methods and Bayesian sensitivity analysis
Eugenia Buta, Hani Doss
Ann. Statist. 39(5): 2658-2685 (October 2011). DOI: 10.1214/11-AOS913


We consider situations in Bayesian analysis where we have a family of priors νh on the parameter θ, where h varies continuously over a space $\mathcal{H}$, and we deal with two related problems. The first involves sensitivity analysis and is stated as follows. Suppose we fix a function f of θ. How do we efficiently estimate the posterior expectation of f(θ) simultaneously for all h in $\mathcal{H}$? The second problem is how do we identify subsets of $\mathcal{H}$ which give rise to reasonable choices of νh? We assume that we are able to generate Markov chain samples from the posterior for a finite number of the priors, and we develop a methodology, based on a combination of importance sampling and the use of control variates, for dealing with these two problems. The methodology applies very generally, and we show how it applies in particular to a commonly used model for variable selection in Bayesian linear regression, and give an illustration on the US crime data of Vandaele.


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Eugenia Buta. Hani Doss. "Computational approaches for empirical Bayes methods and Bayesian sensitivity analysis." Ann. Statist. 39 (5) 2658 - 2685, October 2011.


Published: October 2011
First available in Project Euclid: 22 December 2011

zbMATH: 1231.62008
MathSciNet: MR2906882
Digital Object Identifier: 10.1214/11-AOS913

Primary: 62F15 , 91-08
Secondary: 62F12

Keywords: Bayes factors , control variates , ergodicity , hyperparameter selection , importance sampling , Markov chain Monte Carlo

Rights: Copyright © 2011 Institute of Mathematical Statistics


Vol.39 • No. 5 • October 2011
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