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

2017/11/30 by Patrick J. Laub, Laub, Patrick J., Robert Salomone +3
Computer Science · Decision Sciences · Economics, Econometrics and Finance · #Bayesian Methods and Mixture Models #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Probability and Risk Models #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.1711.11218

openalex publication_date 2017/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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