A simulation-based comparison of maximum entropy and copula methods for capturing non-linear probability dependence

Abstract

The modeling of complex service systems entails capturing many sub-components of the system, and the dependencies that exist among them in the form of a joint probability distribution. Two common methods for constructing joint probability distributions from experts using partial information include maximum entropy methods and copula methods. In this paper we explore the performance of these methods in capturing the dependence between random variables using correlation coefficients and lower-order pairwise assessments. We focus on the case of discrete random variables, and compare the performance of these methods using a Monte Carlo simulation when the variables exhibit both independence and non-linear dependence structures. We show that the maximum entropy method with correlation coefficients and the Gaussian copula method perform similarly, while the maximum entropy method with pairwise assessments performs better particularly when the variables exhibit non-linear dependence.