Note on rejection sampling and exact sampling with the Metropolised independence sampler

Abstract

This short note shows a close relationship between standard rejection sampling and exact sampling by coupling from the past applied to a Metropolised independence sampler. I now know that this idea, first presented as a ten-minute tea-time talk, is probably a duplicate of an unavailable work (Cai 1997), and is closely related to a paper by Jun S. Liu (1996), who provides a much more detailed analysis. Perhaps this exposition will be of interest to some readers.