Conditional Monte Carlo revisited

Abstract

Conditional Monte Carlo refers to sampling from the conditional distribution of a random vector X given the value T ( X ) = t for a function T ( X ) . Classical conditional Monte Carlo methods were designed for estimating conditional expectations of functions ϕ ( X ) by sampling from unconditional distributions obtained by certain weighting schemes. The basic ingredients were the use of importance sampling and change of variables. In the present paper we reformulate the problem by introducing an artificial parametric model in which X is a pivotal quantity, and next representing the conditional distribution of X given T ( X ) = t within this new model. The approach is illustrated by several examples, including a short simulation study and an application to goodness-of-fit testing of real data. The connection to a related approach based on sufficient statistics is briefly discussed.