A Multivariate Statistical Sampling Technique to Enhance Far Quantile Estimates of Arbitrary Responses

We propose a statistical sampling method, called eXtreme Event Sampling (XES), to compute far quantiles of arbitrary responses of multiple independent random parameters more accurately and efficiently than with Classical Monte-Carlo (CMC). Based on the selective over-sampling of events of low probability of occurrence, the method enables the study of multiple responses at a time, unlike the classical Importance Sampling (IS) techniques, expected to be the best-performing when tuned to a single given response. Though more generic than IS, XES still shows large gains over CMC in both accuracy and sampling efficiency, even for a large number of parameters (up to 27 tested). This article presents the detailed theoretical aspects of XES and an empirical study demonstrating its efficiency in various cases of responses (linear or non-linear), distributions (normal and non-normal) and number of parameters. If the primary target application is the design of semiconductor memory circuits, we believe that the flexibility of the method potentially makes it attractive in other contexts showing similar constraints.