Sequential design of experiments for estimating percentiles of black-box functions

2016/05/18 by Tatiana Labopin-Richard, Labopin-Richard, T, Victor Picheny +1
Computer Science · Decision Sciences · #Advanced Multi-Objective Optimization Algorithms #FOS: Mathematics #Gaussian Processes and Bayesian Inference #Optimal Experimental Design Methods #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.1605.05524

openalex publication_date 2016/05/18 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

Estimating percentiles of black-box deterministic functions with random inputs is a challenging task when the number of function evaluations is severely restricted, which is typical for computer experiments. This article proposes two new sequential Bayesian methods for percentile estimation based on the Gaussian Process metamodel. Both rely on the Stepwise Uncertainty Reduction paradigm, hence aim at providing a sequence of function evaluations that reduces an uncertainty measure associated with the percentile estimator. The proposed strategies are tested on several numerical examples, showing that accurate estimators can be obtained using only a small number of functions evaluations.

Citations

• On the limited memory BFGS method for large scale optimization
• Sequential design of computer experiments for the estimation of a probability of failure

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