Distributionally Robust Monte Carlo Simulation: An Introduction to a New Line of Research

Whereas the use of traditional Monte Carlo simulation requires probability distributions for the uncertain parameters entering the system,  distributionally robust  Monte Carlo simulation does not. The description of this new approach to Monte Carlo simulation is the focal point of this seminar. According to the new theory, instead of carrying out simulations using some rather arbitrary probability distribution such as Gaussian, for the uncertain parameters, we provide a rather different prescription based on  distributional robustness  considerations. The new approach which we describe, does not require a probability distribution   f   for the uncertainty. Instead, based on manufacturing considerations, a class of distributions   F   is specified and the satisfaction of the probabilistic requirement must be satisfied for all   f   in  F . In a sense, this new method of Monte Carlo simulation was developed with the robustician in mind. That is, the motivation for this new approach is derived from the fact that robusticians often object to classical Monte Carlo simulation on the grounds that the probability distribution for the uncertain parameters is unavailable. They typically begin only with bounds on the uncertain parameters and are unwilling to assume an a  priori  probability distribution. This is the same starting point for the methods provided here.