The double CFTP method

Abstract

We consider the problem of the exact simulation of random variables Z that satisfy the distributional identity Z = L VY + (1- V ) Z , where V ∈ [0,1] and Y are independent, and = L denotes equality in distribution. Equivalently, Z is the limit of a Markov chain driven by that map. We give an algorithm that can be automated under the condition that we have a source capable of generating independent copies of Y , and that V has a density that can be evaluated in a black-box format. The method uses a doubling trick for inducing coalescence in coupling from the past. Applications include exact samplers for many Dirichlet means, some two-parameter Poisson--Dirichlet means, and a host of other distributions related to occupation times of Bessel bridges that can be described by stochastic fixed point equations.