Échantillonnage préférentiel et méta-modèles : méthodes bayésiennes optimale et défensive

Abstract : This paper considers the problem of the choice of an instrumental distribution for the estimation by preferential sampling of an integral $\int h(x) \pi(x)\, {\rm d}x $, where the function $h$ is expensive to evaluate. To build such an instrumental distribution, we adopt a Bayesian approach where we introduce a prior about $h$, which makes it possible to construct a Bayes-optimal instrumental distribution, given evaluation results of $h$. This instrumental distribution minimizes the expectation (with respect to the prior distribution about $h$) of the (frequentist) variance of estimation. However, the variance of estimation obtained using this instrumental distribution can be larger than that of the Monte Carlo estimator in some cases. We present a "defensive" correction of the Bayes-optimal instrumental distribution to address this issue. We illustrate the approach on a problem of estimation of a probability of failure, based on an industrial numerical simulator from the domain of structural reliability.
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Submitted on : Monday, June 15, 2015 - 11:01:19 AM
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Julien Bect, Roman Sueur, Alexis Gérossier, Loïc Mongellaz, Sébastien Petit, et al.. Échantillonnage préférentiel et méta-modèles : méthodes bayésiennes optimale et défensive. 47èmes Journées de Statistique de la SFdS (JdS 2015), Jun 2015, Lille, France. ⟨hal-01163632⟩

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