Title: Monte Carlo Estimation of the Density of the Sum of Dependent Random Variables,
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.