Optimal oversampling ratio in two-step simulation

Abstract

This paper analyses a novel two-step Monte Carlo simulation algorithm to estimate the weighted volume of a polytope of the form Az≤T . The essential idea is to partition the columns of A into two categories – a lightweight category and a heavyweight category. Simulation is done in a two-step manner where, for every sample of the lightweight category variables we use multiple samples of the heavyweight category variables. Thus, the heavyweight category variables are oversampled with respect to the lightweight category variables and increasing samples of the heavyweight variables at the expense of the lightweight variables will lead to a more efficient Monte Carlo method. In this paper we present a fast heuristic approximate for estimating the optimal oversampling ratio and substantiate with experimental results which confirm the effectiveness of the method.