Randal Douc 
(joint work with Christian P. Robert)

Telecom Sud Paris

A VANILLA RAO-BLACKWELLISATION OF METROPOLIS-HASTINGS ALGORITHMS

Abstract

Casella and Robert (1996) presented a general Rao-Blackwellisa-
tion principle for accept-reject and Metropolis-Hastings schemes that
leads to significant decreases in the variance of the resulting estima-
tors, but at a high cost in computing and storage. Adopting a com-
pletely different perspective, we introduce instead a universal scheme
that guarantees variance reductions in all Metropolis-Hastings based
estimators while keeping the computing cost under control. We es-
tablish a central limit theorems for the improved estimators and il-
lustrate their performances on toy examples.