Statistics – Computation
Scientific paper
2010-09-27
Statistics and Computing, 22(3):773-793, 2012
Statistics
Computation
This is an author-generated postprint version. The published version is available at http://www.springerlink.com
Scientific paper
10.1007/s11222-011-9241-4
This paper deals with the problem of estimating the volume of the excursion set of a function $f:\mathbb{R}^d \to \mathbb{R}$ above a given threshold, under a probability measure on $\mathbb{R}^d$ that is assumed to be known. In the industrial world, this corresponds to the problem of estimating a probability of failure of a system. When only an expensive-to-simulate model of the system is available, the budget for simulations is usually severely limited and therefore classical Monte Carlo methods ought to be avoided. One of the main contributions of this article is to derive SUR (stepwise uncertainty reduction) strategies from a Bayesian-theoretic formulation of the problem of estimating a probability of failure. These sequential strategies use a Gaussian process model of $f$ and aim at performing evaluations of $f$ as efficiently as possible to infer the value of the probability of failure. We compare these strategies to other strategies also based on a Gaussian process model for estimating a probability of failure.
Bect Julien
Ginsbourger David
Li Ling
Picheny Victor
Vazquez Emmanuel
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