Asymptotic Consistency of Loss-Calibrated Variational Bayes

Abstract

This paper establishes the asymptotic consistency of the loss-calibrated variational Bayes (LCVB) method. LCVB was proposed in~LaSiGh2011 as a method for approximately computing Bayesian posteriors in a `loss aware' manner. This methodology is also highly relevant in general data-driven decision-making contexts. Here, we not only establish the asymptotic consistency of the calibrated approximate posterior, but also the asymptotic consistency of decision rules. We also establish the asymptotic consistency of decision rules obtained from a `naive' variational Bayesian procedure.

Tasks

Reproductions