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

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 est...

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Bibliographic Details
Published in:Statistics and computing 2012-05, Vol.22 (3), p.809-821
Main Authors: Munoz Zuniga, Miguel, Garnier, Josselin, Remy, Emmanuel, de Rocquigny, Etienne
Format: Article
Language:English
Subjects:
Artificial Intelligence
Mathematics
Mathematics and Statistics
Probability
Probability and Statistics in Computer Science
Statistical Theory and Methods
Statistics
Statistics and Computing/Statistics Programs
Statistics Theory
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Summary: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.
ISSN:0960-3174
1573-1375
DOI:10.1007/s11222-011-9277-5