Using Orthogonal Arrays in the Sensitivity Analysis of Computer Models
We consider a class of input sampling plans, called permuted column sampling plans, that are popular in sensitivity analysis of computer models. Permuted column plans, including replicated Latin hypercube sampling, support estimation of first-order sensitivity coefficients, but these estimates are b...
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Published in | Technometrics Vol. 50; no. 2; pp. 205 - 215 |
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Main Authors | , , |
Format | Journal Article |
Language | English |
Published |
Alexandria, VI
Taylor & Francis
01.05.2008
Milwaukee, WI The American Society for Quality and The American Statistical Association American Society for Quality Control American Statistical Association American Society for Quality |
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Abstract | We consider a class of input sampling plans, called permuted column sampling plans, that are popular in sensitivity analysis of computer models. Permuted column plans, including replicated Latin hypercube sampling, support estimation of first-order sensitivity coefficients, but these estimates are biased when the usual practice of random column permutation is used to construct the sampling arrays. Deterministic column permutations may be used to eliminate this estimation bias. We prove that any permuted column sampling plan that eliminates estimation bias, using the smallest possible number of runs in each array and containing the largest possible number of arrays, can be characterized by an orthogonal array of strength 2. We derive approximate standard errors of the first-order sensitivityindices for this sampling plan. We give two examples demonstrating the sampling plan, behavior of the estimates, and standard errors, along with comparative results based on other approaches. |
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AbstractList | We consider a class of input sampling plans, called permuted column sampling plans, that are popular in sensitivity analysis of computer models. Permuted column plans, including replicated Latin hypercube sampling, support estimation of first-order sensitivity coefficients, but these estimates are biased when the usual practice of random column permutation is used to construct the sampling arrays. Deterministic column permutations may be used to eliminate this estimation bias. We prove that any permuted column sampling plan that eliminates estimation bias, using the smallest possible number of runs in each array and containing the largest possible number of arrays, can be characterized by an orthogonal array of strength 2. We derive approximate standard errors of the first-order sensitivity indices for this sampling plan. We give two examples demonstrating the sampling plan, behavior of the estimates, and standard errors, along with comparative results based on other approaches. We consider a class of input sampling plans, called permuted column sampling plans, that are popular in sensitivity analysis of computer models. Permuted column plans, including replicated Latin hypercube sampling, support estimation of first-order sensitivity coefficients, but these estimates are biased when the usual practice of random column permutation is used to construct the sampling arrays. Deterministic column permutations may be used to eliminate this estimation bias. We prove that any permuted column sampling plan that eliminates estimation bias, using the smallest possible number of runs in each array and containing the largest possible number of arrays, can be characterized by an orthogonal array of strength 2. We derive approximate standard errors of the first-order sensitivity indices for this sampling plan. We give two examples demonstrating the sampling plan, behavior of the estimates, and standard errors, along with comparative results based on other approaches. [PUBLICATION ABSTRACT] We consider a class of input sampling plans, called permuted column sampling plans, that are popular in sensitivity analysis of computer models. Permuted column plans, including replicated Latin hypercube sampling, support estimation of first-order sensitivity coefficients, but these estimates are biased when the usual practice of random column permutation is used to construct the sampling arrays. Deterministic column permutations may be used to eliminate this estimation bias. We prove that any permuted column sampling plan that eliminates estimation bias, using the smallest possible number of runs in each array and containing the largest possible number of arrays, can be characterized by an orthogonal array of strength 2. We derive approximate standard errors of the first-order sensitivityindices for this sampling plan. We give two examples demonstrating the sampling plan, behavior of the estimates, and standard errors, along with comparative results based on other approaches. |
Author | Moore, Leslie M. Morris, Max D. McKay, Michael D. |
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Cites_doi | 10.1080/00949659708811825 10.1016/0951-8320(95)00099-2 10.2307/1268522 10.1111/j.1467-9868.2004.05304.x 10.2307/2291014 10.1016/j.ress.2005.06.003 10.1016/S0010-4655(02)00280-1 10.1063/1.1680571 10.1098/rspl.1902.0099 10.1016/j.cpc.2007.07.011 10.2307/1269769 10.2307/2291282 10.2307/1266466 10.1016/j.jspi.2005.01.001 10.1214/aoms/1177730196 |
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Keywords | Sensitivity analysis Probabilistic approach Error estimation Computer simulation First-order variance coefficient Permutation Bias Replicated Latin hypercube sample Modeling Optimization Variance Uncertain system Latin hypercube sampling Computer experiment Experimental design Deterministic approach Uncertainty analysis Biased estimation |
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References | p_16 p_18 p_1 p_12 p_23 p_3 p_13 p_14 p_5 p_15 p_8 p_7 Sobol' I. M. (p_19) 1993; 1 Owen A. (p_11) 1992; 2 p_20 p_10 p_22 |
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SubjectTerms | Arrays Bias Computer experiment Computer modeling Environment modeling Estimates Estimation bias Exact sciences and technology Experimental design First-order variance coefficient Mathematical functions Mathematics Modeling Probability and statistics Random sampling Replicated Latin hypercube sample Sample variance Sampling theory, sample surveys Sciences and techniques of general use Sensitivity analysis Standard error Statistical variance Statistics Studies Uncertainty analysis |
Title | Using Orthogonal Arrays in the Sensitivity Analysis of Computer Models |
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