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

Abstract

Various 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.