A Class Coupler for Perfect Sampling from Continuous Distributions With and Without Atoms

TL;DR

This paper introduces a versatile 'class coupler' algorithm for perfect sampling from mixed discrete-continuous distributions, extending existing methods to broader cases and demonstrating its effectiveness in Bayesian hypothesis testing.

Contribution

It extends a Metropolis-Hastings-based perfect sampling algorithm to handle a wider class of distributions, including pure discrete and continuous cases, with practical Bayesian applications.

Findings

Algorithm is fast to implement

Applicable to pure discrete and continuous densities

Effective in Bayesian posterior simulation

Abstract

We consider the simulation of distributions that are a mixture of discrete and continuous components. We extend a Metropolis-Hastings-based perfect sampling algorithm of Corcoran and Tweedie to allow for a broader class of transition candidate densities. The resulting algorithm, know as a "class coupler", is fast to implement and is applicable to purely discrete or purely continuous densities as well. Our work is motivated by the study of a composite hypothesis test in a Bayesian setting via posterior simulation and we give simulation results for some problems in this area.