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Gustafson, Paul; Wasserman, Larry

Local sensitivity diagnostics for Bayesian inference. (English) Zbl 0854.62024

Ann. Stat. 23, No. 6, 2153-2167 (1995).
Summary: 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 \(\varphi\)-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.

Cited in 31 Documents

MSC:

62F15 Bayesian inference
62F35 Robustness and adaptive procedures (parametric inference)

Keywords:

classes of probabilities; Frechet derivatives; Kullback-Leibler distance; Hellinger distance; robustness; total variation distance; multiparameter models; diagnostics; prior; density ratio topology
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References:

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