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December 1995 Local sensitivity diagnostics for Bayesian inference
Paul Gustafson, Larry Wasserman
Ann. Statist. 23(6): 2153-2167 (December 1995). DOI: 10.1214/aos/1034713652

Abstract

We investigate diagnostics for quantifying the effect of small changes to the prior distribution over a k-dimensional parameter space. We show that several previously suggested diagnostics, such as the norm of the Fréchet derivative, diverge at rate $n^{k/2}$ if the base prior is an interior point in the class of priors, under the density ratio topology. Diagnostics based on $\phi$-divergences exhibit similar asymptotic behavior. We show that better asymptotic behavior can be obtained by suitably restricting the classes of priors. We also extend the diagnostics to see how various marginals of the prior affect various marginals of the posterior.

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Paul Gustafson. Larry Wasserman. "Local sensitivity diagnostics for Bayesian inference." Ann. Statist. 23 (6) 2153 - 2167, December 1995. https://doi.org/10.1214/aos/1034713652

Information

Published: December 1995
First available in Project Euclid: 15 October 2002

zbMATH: 0854.62024
MathSciNet: MR1389870
Digital Object Identifier: 10.1214/aos/1034713652

Subjects:
Primary: 62F15
Secondary: 62F35

Rights: Copyright © 1995 Institute of Mathematical Statistics

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Vol.23 • No. 6 • December 1995
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