Conditional Monte Carlo revisited

TL;DR

This paper revisits Conditional Monte Carlo methods by introducing an artificial parametric model to facilitate sampling from conditional distributions, demonstrated through examples, simulations, and a real data application.

Contribution

It proposes a novel reformulation of Conditional Monte Carlo using an artificial parametric model to improve conditional sampling techniques.

Findings

Effective sampling from complex conditional distributions demonstrated

Simulation studies validate the proposed approach

Application to real data shows practical utility

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 of 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, representing the conditional distribution of X given T(X)=t within this new model. The key is to provide the parameter of the artificial model by a distribution. The approach is illustrated by several examples, which are particularly chosen to illustrate conditional sampling in cases where such sampling is not straightforward. A simulation study and an application to goodness-of-fit testing of real data are also given.