Empirical model-building and response surface
Empirical model-building and response surface
Numerical recipes in C (2nd ed.): the art of scientific computing
Numerical recipes in C (2nd ed.): the art of scientific computing
Screening, predicting, and computer experiments
Technometrics
Dynamic Programming and Optimal Control
Dynamic Programming and Optimal Control
Efficient Global Optimization of Expensive Black-Box Functions
Journal of Global Optimization
A Knowledge-Gradient Policy for Sequential Information Collection
SIAM Journal on Control and Optimization
An informational approach to the global optimization of expensive-to-evaluate functions
Journal of Global Optimization
Adaptive virtual support vector machine for reliability analysis of high-dimensional problems
Structural and Multidisciplinary Optimization
Computational Statistics & Data Analysis
Noisy kriging-based optimization methods: A unified implementation within the DiceOptim package
Computational Statistics & Data Analysis
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This paper deals with the problem of estimating the volume of the excursion set of a function f:驴 d 驴驴 above a given threshold, under a probability measure on 驴 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 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.