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We propose a geometric framework to assess sensitivity of Bayesian proceduresto modeling assumptions based on the nonparametric Fisher-Rao metric. While theframework is general in spirit, the focus of this article is restricted tometric-based diagnosis under two settings: assessing local and globalrobustness in Bayesian procedures to perturbations of the likelihood and prior,and identification of influential observations. The approach is based on thesquare-root representation of densities which enables one to compute geodesicsand geodesic distances in analytical form, facilitating the definition ofnaturally calibrated local and global discrepancy measures. An importantfeature of our approach is the definition of a geometric$\epsilon$-contamination class of sampling distributions and priors viaintrinsic analysis on the space of probability density functions. We showcasethe applicability of our framework on several simulated toy datasets as well asin real data settings for generalized mixed effects models, directional dataand shape data.

Bayes Sensitivity with Fisher-Rao Metric