The Annals of Statistics

Local sensitivity diagnostics for Bayesian inference

Paul Gustafson and Larry Wasserman

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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.

Article information

Ann. Statist., Volume 23, Number 6 (1995), 2153-2167.

First available in Project Euclid: 15 October 2002

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62F15: Bayesian inference
Secondary: 62F35: Robustness and adaptive procedures

Classes of probabilities $\phi$-divergence Fréchet derivatives Kullback-Leibler distance Hellinger distance robustness total variation distance


Gustafson, Paul; Wasserman, Larry. Local sensitivity diagnostics for Bayesian inference. Ann. Statist. 23 (1995), no. 6, 2153--2167. doi:10.1214/aos/1034713652.

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