Efficient computation of global sensitivity indices using sparse polynomial chaos expansions
TL;DR: Sparse polynomial chaos (PC) expansions are introduced in order to compute sensitivity indices and a bootstrap technique is developed which eventually yields confidence intervals on the results.
About: This article is published in Reliability Engineering & System Safety.The article was published on 2010-11-01. It has received 332 citations till now. The article focuses on the topics: Sobol sequence & Monte Carlo method.
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TL;DR: A non intrusive method that builds a sparse PC expansion, which may be obtained at a reduced computational cost compared to the classical ''full'' PC approximation.
1,112 citations
TL;DR: A non-intrusive method that builds a sparse PC expansion and an adaptive regression-based algorithm is proposed for automatically detecting the significant coefficients of the PC expansion in a suitable polynomial chaos basis.
710 citations
TL;DR: This work investigates in detail the methodological issues concerning the crucial step of correctly interpreting the results of a sensitivity analysis, and presents recent results that permit the estimation of global sensitivity measures by post-processing the sample generated by a traditional Monte Carlo simulation.
673 citations
TL;DR: Two broad families of surrogates namely response surface surrogates, which are statistical or empirical data‐driven models emulating the high‐fidelity model responses, and lower‐f fidelity physically based surrogates which are simplified models of the original system are detailed in this paper.
Abstract: [1] Surrogate modeling, also called metamodeling, has evolved and been extensively used over the past decades. A wide variety of methods and tools have been introduced for surrogate modeling aiming to develop and utilize computationally more efficient surrogates of high-fidelity models mostly in optimization frameworks. This paper reviews, analyzes, and categorizes research efforts on surrogate modeling and applications with an emphasis on the research accomplished in the water resources field. The review analyzes 48 references on surrogate modeling arising from water resources and also screens out more than 100 references from the broader research community. Two broad families of surrogates namely response surface surrogates, which are statistical or empirical data-driven models emulating the high-fidelity model responses, and lower-fidelity physically based surrogates, which are simplified models of the original system, are detailed in this paper. Taxonomies on surrogate modeling frameworks, practical details, advances, challenges, and limitations are outlined. Important observations and some guidance for surrogate modeling decisions are provided along with a list of important future research directions that would benefit the common sampling and search (optimization) analyses found in water resources.
663 citations
TL;DR: The key idea is to align the complexity level and order of analysis with the reliability and detail level of statistical information on the input parameters to avoid the necessity to assign parametric probability distributions that are not sufficiently supported by limited available data.
350 citations
References
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01 Jan 1993TL;DR: This article presents bootstrap methods for estimation, using simple arguments, with Minitab macros for implementing these methods, as well as some examples of how these methods could be used for estimation purposes.
Abstract: This article presents bootstrap methods for estimation, using simple arguments. Minitab macros for implementing these methods are given.
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TL;DR: In this paper, two sampling plans are examined as alternatives to simple random sampling in Monte Carlo studies and they are shown to be improvements over simple sampling with respect to variance for a class of estimators which includes the sample mean and the empirical distribution function.
Abstract: Two types of sampling plans are examined as alternatives to simple random sampling in Monte Carlo studies. These plans are shown to be improvements over simple random sampling with respect to variance for a class of estimators which includes the sample mean and the empirical distribution function.
8,328 citations
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20 Dec 1990TL;DR: In this article, a representation of stochastic processes and response statistics are represented by finite element method and response representation, respectively, and numerical examples are provided for each of them.
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5,495 citations