Local Sensitivity Diagnostics
for Bayesian Inference
We investigate diagnostics for quantifying the effect of small changes
to the prior distribution. We show that several previously suggested
diagnostics, such as the norm of the Fréchet derivative, diverge
at rate if the base prior is an interior point in the class
of priors, under the density ratio topology. Diagnostics based on
-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 multiparameter
models. This allows us to see how various marginals of the prior
affect various marginals of the posterior.
KEY WORDS AND PHRASES: Classes of probabilities;
-divergence; Fréchet derivatives; Kullback-Leibler distance;
Hellinger distance; Robustness; Total variation distance.