Analysis of adaptive directional stratification for the controlled estimation of rare event probabilities

Authors:
Miguel Munoz Zuniga;Josselin Garnier;Emmanuel Remy;Etienne Rocquigny
Affiliations:
Laboratoire de Probabilités et Modèles Aléatoires, Université Paris VII, Paris cedex 05, France 75251;Laboratoire de Probabilités et Modèles Aléatoires, Université Paris VII, Paris cedex 05, France 75251;EDF R&D, Chatou, France 78400;Ecole Centrale de Paris, Chatenay-Malabry, France 92295
Venue:
Statistics and Computing
Year:
2012

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Abstract

In the context of structural reliability, a small probability to be assessed, a high computational time model and a relatively large input dimension are typical constraints which brought together lead to an interesting challenge. Indeed, in this framework many existing stochastic methods fail in estimating the failure probability with robustness.Therefore, the aim of this article is to present and prove theoretical results about the validity of an original method we have introduced to overcome the specific constraints mentioned above. This new method turns out to be competitive compared with the existing techniques. It is a variant of accelerated Monte Carlo simulation method, named ADS-2--Adaptive Directional Stratification. It combines, in a two steps adaptive strategy, the stratification into quadrants and the directional simulation techniques. Two ADS-2 estimators are presented and their properties are studied.