Title
Bayesian Sensitivity Analysis with Fisher-Rao Metric
Speaker
Sebastian Kurtek, The Ohio State University
Abstract
We present a geometric framework to assess sensitivity of Bayesian procedures to modeling assumptions based on the nonparametric Fisher-Rao metric. While the framework is general in spirit, the focus of this talk is restricted to metric-based diagnosis under two settings: assessing local and global robustness in Bayesian procedures to perturbations of the likelihood and prior, and identification of influential observations. The approach is based on the square-root representation of densities which enables one to compute geodesics and geodesic distances in analytical form, facilitating the definition of naturally calibrated local and global discrepancy measures. An important feature of this approach is the definition of a geometric contamination class of sampling distributions and priors via intrinsic analysis on the space of probability density functions. We showcase the applicability of our framework on several simulated toy datasets as well as in real data settings for generalized mixed effects models, directional data and shape data.
