Statistics and Probability Seminar: Riemannian framework for Bayes robustness and Variational Bayes

Riemannian framework for Bayes robustness and Variational Bayes

Karthik Bharath (University of Nottingham)

A Riemannian-geometric framework is proposed to assess sensitivity of Bayesian procedures to modelling assumptions based on the nonparametric Fisher-Rao metric; assessments include local and global robustness to perturbations of the likelihood and prior, and identification of influential observations. The motivation lies in the unification of the perturbation and the inference via intrinsic analysis on the space of probability densities under the same Riemannian metric which leads to geometrically calibrated influence measures. Additionally, the use of the framework in Variational approaches to posterior approximation will be discussed.