Generalized Accept-Reject sampling schemes

George Casella, Christian P. Robert, Martin T. Wells

Source: Anirban DasGupta, ed., A Festschrift for Herman Rubin (Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2004), 342-347.

Abstract

This paper extends the Accept-Reject algorithm to allow the proposal distribution to change at each iteration. We first establish a necessary and sufficient condition for this generalized Accept-Reject algorithm to be valid, and then show how the resulting estimator can be improved by Rao-Blackwellization. An application of these results is to the perfect sampling technique of Fill (1998), An interruptible algorithm for perfect sampling via Markov chains, which is a generalized Accept-Reject algorithm.