Plug-in estimation of d-dimensional density minimum volume set of a rare event in a complex system

Abstract

International audienceVarious reliability or hedging problems boil down to quantile estimation. However, real-life systems are usually multidimensional and thus often imply multidimensional density minimum volume set estimation which is usually done with Monte Carlo simulations. Increasing safety standards create a need for density minimum volume set estimation with low probability that crude Monte Carlo cannot fulfil. This paper proposes a new importance sampling algorithm that estimates efficiently multidimensional density minimum volume sets for extreme probability. It also presents some numerical results on a simple bidimensional Gaussian case and on a realistic launcher impact safety zone estimation

Drone Ground Impact Footprints with Importance Sampling: Estimation and Sensitivity Analysis

“…The principle of importance sampling is to modify the sampling distribution of Z i , in order to improve the accuracy of the estimation of g on some part of its support. A comparison between Monte Carlo and classical importance sampling estimates of g is indeed performed in [17]. Depending on the value of α, a trade-off should be made.…”