Projection Pursuit Multivariate Sampling of Parameter Uncertainty

Abstract

The efficiency of sampling is a critical concern in Monte Carlo analysis, which is frequently used to assess the effect of the uncertainty of the input variables on the uncertainty of the model outputs. The projection pursuit multivariate transform is proposed as an easily applicable tool for improving the efficiency and quality of a sampling design in Monte Carlo analysis. The superiority of the projection pursuit multivariate transform, as a sampling technique, is demonstrated in two synthetic case studies, where the random variables are considered to be uncorrelated and correlated in low (bivariate) and high (five-variate) dimensional sampling spaces. Five sampling techniques including Monte Carlo simulation, classic Latin hypercube sampling, maximin Latin hypercube sampling, Latin hypercube sampling with multidimensional uniformity, and projection pursuit multivariate transform are employed in the simulation studies, considering cases where the sample sizes (n) are small (i.e., 10≤n≤100), medium (i.e., 100<n≤1000), and large (i.e., 1000 < n≤ 10,000). The results of the case studies show that the projection pursuit multivariate transform appears to yield the fewest sampling errors and the best sampling space coverage (or multidimensional uniformity), and that a significant amount of computer effort could be saved by using this technique.