Bernstein adaptive nonparametric conditional sampling: a new method for rare event probability estimation

Abstract

Reliability analysis often requires estimating small failure probabilities, associated with rare events. To overcome their intractable crude Monte Carlo estimation, various techniques have been proposed. Among others, ``subset sampling'' divides the rare event into a set of nested conditional events, individually easier to assess. At each iteration, subset sampling generates conditional samples by Markov chain Monte Carlo, mechanically making the samples dependent. The present work introduces a new rare event estimation method, adopting the same structure as subset sampling while using a different approach to generate intermediary conditional samples. This method intends to fit the complex intermediary conditional distributions with a nonparametric modeling tool called ``Empirical Bernstein Copula''. Then, the explicit models fitted allow direct Monte Carlo sampling. Unlike Markov chain Monte Carlo sampling, this approach allows i.i.d sampling on intermediary conditional distributions. This property is important to fully exploit recent development related to reliability-oriented sensitivity analysis.