A Bayesian Edgeworth Expansion and its Applications

Abstract

The Edgeworth expansion has existed for over a century, but there is no corresponding expansion in Bayesian statistics. This talk presents an Edgeworth type expansion for posterior distributions by using a version of Stein's Identity and properties of Hermite polynomials. We also show that such expansions can be used in validating convergence of MCMC results. Some examples are provided for illustration.