Thursday, September 10, 2015 - 3:00pm
Cockins Hall (CH), Room 240
Reconciling Two Popular Approaches for Summarizing Case Influence in Bayesian Models
Mario Peruggia, The Ohio State University
Methods for summarizing case influence in Bayesian models take essentially two forms: (1) use common divergence measures for calculating distances between full-data posteriors and case-deleted posteriors, and (2) measure the impact of infinitesimal perturbations to the likelihood to gain information about local case influence. Methods based on approach (1) lead naturally to considering the behavior of case-deletion importance sampling weights (the weights used to approximate samples from the case-deleted posterior using samples from the full posterior). Methods based on approach (2) lead naturally to considering the curvature of the Kullback-Leibler divergence of the full posterior from the case-deleted posterior. By examining the connections between the two approaches, we establish a rationale for employing low-dimensional summaries of case influence that are obtained entirely via the variance-covariance matrix of the log importance sampling weights.
This is joint work with Zachary Thomas and Steven MacEachern.