Using Orthogonal Arrays in the Sensitivity Analysis of Computer Models

• Published in: Technometrics Vol. 50; no. 2; pp. 205 - 215
• Main Authors: Morris, Max D., Moore, Leslie M., McKay, Michael D.
• 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
• Subjects: 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; 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
• DOI: 10.1198/004017008000000208
• ISSN: 0040-1706

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.