Evaluating improper priors and the recurrence of symmetric Markov chains: an overview

Morris L. Eaton

Source: Anirban DasGupta, ed., A Festschrift for Herman Rubin (Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2004), 5-20.

Abstract

Given a parametric statistical model, an improper prior distribution can often be used to induce a proper posterior distribution (an inference). This inference can then be used to solve decision problems once an action space and loss have been specified. One way to evaluate the inference is to ask for which estimation problems does the above formal Bayes method produce admissible estimators. The relationship of this problem to the recurrence of an associated symmetric Markov chain is reviewed.