Conference Program Home
  My Program

All Times EDT

Abstract Details

Activity Number: 191 - Misspecification and Robustness: Novel Methods and Innovative Insights
Type: Topic Contributed
Date/Time: Monday, August 8, 2022 : 2:00 PM to 3:50 PM
Sponsor: International Society for Bayesian Analysis (ISBA)
Abstract #322815
Title: On the Robustness to Misspecification of Alpha-Posteriors and Their Variational Approximations
Author(s): Marco Avella Medina* and Cynthia Rush and Jose Luis Montiel Olea and Amilcar Velez
Companies: Columbia University and Columbia University and Columbia University and Northwestern University
Keywords: alpha-posterior ; variational inference; model misspecification; robustness

Alpha-posteriors and their variational approximations distort standard posterior inference by downweighting the likelihood and introducing variational approximation errors. We show that such distortions, if tuned appropriately, reduce the Kullback-Leibler (KL) divergence from the true, but perhaps infeasible, posterior distribution when there is potential parametric model misspecification. To make this point, we derive a Bernstein-von Mises theorem showing convergence in total variation distance of alpha-posteriors and their variational approximations to limiting Gaussian distributions. We use these distributions to evaluate the KL divergence between true and reported posteriors. We show this divergence is minimized by choosing alpha strictly smaller than one, assuming there is a vanishingly small probability of model misspecification. The optimized value becomes smaller as the the misspecification becomes more severe. The optimized KL divergence increases logarithmically in the degree of misspecification and not linearly as with the usual posterior.

Authors who are presenting talks have a * after their name.

Back to the full JSM 2022 program