Monte Carlo Estimation of the Density of the Sum of Dependent Random Variables

TL;DR

This paper introduces an unbiased Monte Carlo estimator for the density of a sum of dependent random variables, demonstrating its effectiveness through numerical studies and applications in Bayesian statistics.

Contribution

It proposes a novel unbiased estimator for the density of sums of dependent variables, extending to Bayesian marginal density estimation and Gaussian copula dependence.

Findings

Estimator performs favorably in variance compared to existing methods

Numerical studies validate the estimator's efficiency

Applications demonstrate practical utility in Bayesian contexts

Abstract

We study an unbiased estimator for the density of a sum of random variables that are simulated from a computer model. A numerical study on examples with copula dependence is conducted where the proposed estimator performs favourably in terms of variance compared to other unbiased estimators. We provide applications and extensions to the estimation of marginal densities in Bayesian statistics and to the estimation of the density of sums of random variables under Gaussian copula dependence.