Design and Modeling for Computer Experiments
Computer simulations based on mathematical models have become ubiquitous across the engineering disciplines and throughout the physical sciences. Successful use of a simulation model, however, requires careful interrogation of the model through systematic computer experiments. While specific theoretical/mathematical examinations of computer experiment design are available, those interested in applying proposed methodologies need a practical presentation and straightforward guidance on analyzing and interpreting experiment results.
Written by authors with strong academic reputations and real-world practical experience, Design and Modeling for Computer Experiments is exactly the kind of treatment you need. The authors blend a sound, modern statistical approach with extensive engineering applications and clearly delineate the steps required to successfully model a problem and provide an analysis that will help find the solution. Part I introduces the design and modeling of computer experiments and the basic concepts used throughout the book. Part II focuses on the design of computer experiments. The authors present the most popular space-filling designs - like Latin hypercube sampling and its modifications and uniform design - including their definitions, properties, construction and related generating algorithms. Part III discusses the modeling of data from computer experiments. Here the authors present various modeling techniques and discuss model interpretation, including sensitivity analysis. An appendix reviews the statistics and mathematics concepts needed, and numerous examples clarify the techniques and their implementation.
The complexity of real physical systems means that there is usually no simple analytic formula that sufficiently describes the phenomena. Useful both as a textbook and professional reference, this book presents the techniques you need to design and model computer experiments for practical problem solving.
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Designs for Computer Experiments
Latin Hypercube Sampling and Its Modifications
Uniform Experimental Design
Optimization in Construction of Designs for Computer Experiments
Modeling for Computer Experiments
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ANOVA approach basis functions Bayesian categorical discrepancy CD-value Chapter coefficient column construction correlation function covariance Crank Angle criterion cross validation data set defined denoted design space distribution Dnew engine example experimental domain factorial design factors Fang Figure functional linear model Gaussian Kriging model Gaussian process glp method input variables introduced iteration L2-discrepancy Latin hypercube sampling Latin square least squares estimate level-combinations likelihood function linear regression log-likelihood lower bound main effects matrix mean square error measure of uniformity metamodel minimize modeling computer experiments number of runs orthogonal array output parameter penalized least squares plots polynomial basis polynomial model polynomial regression proposed quasi-Monte Carlo methods radial basis function random error regression model resulting estimate SCAD Section simulation space-filling designs spline star discrepancy statistical Step Sudjianto sum of squares Table true model U-type design uniform design variance vector Winker
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Page 264 - A method for exact calculation of the discrepancy of low-dimensional finite point sets I.