Design and Analysis of Computer Experiments

AvThomas J. Santner,Brian J. Williams

Häftad, Engelska, 2010

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Beskrivning

In the past 15 to 20 years, the computer has become a popular tool for exploring the relationship between a measured response and factors thought to affect the response. In many cases, scientific theories exist that implicitly relate the response to the factors by means of systems of mathematical equations. There also exist numerical methods for accurately solving such equations and appropriate computer hardware and software to implement these methods. In many engineering applications, for example, the relationship is described by a dynamical system and the numerical method is a finite element code. In such situations, these numerical methods allow one to produce computer code that can generate the response corresponding to any given set of values of the factors. This allows one to conduct an "experiment" (called a "computer experiment") to explore the relationship between the response and the factors using the code. Indeed, in some cases computer experimentation is feasible when a properly designed physical experiment (the gold standard for establishing cause and effect) is impossible. For example, the number of input variables may be too large to consider performing a physical experiment or it may simply be economically prohibitive to run an experiment on the scale required to gather sufficient information to answer a particular research question. This book describes methods for designing and analyzing experiments conducted using computer code in lieu of a physical experiment. It discusses how to select the values of the factors at which to run the code (the design of the computer experiment) in light of the research objectives of the experimenter. It also provides techniques for analyzing the resulting data so as to achieve these research goals.

Produktinformation

Utgivningsdatum:2010-12-01
Mått:155 x 235 x undefined mm
Vikt:459 g
Format:Häftad
Språk:Engelska
Serie:Springer Series in Statistics
Antal sidor:284
Förlag:Springer-Verlag New York Inc.
ISBN:9781441929921

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Recensioner i media

From the reviews: "This is quite a unique book and may fill a void in the design of experiments literature." Techonmetrics, November 2004 "This book will be a valuable reference for for any statistitican who is collaborating with scientists who use computer experiments or is interested in pursuing research in the area." Biometrics, March 2005 "This book describes methods for designing and analyzing experiments conducted using computer program to replace a physical experiment. ... To the best of my knowledge, there has been no book yet written in the area of computer experiment. ... Therefore, this is quite a unique book and may fill a void in the design of experiments literature. As mentioned in the Preface, this book has tried to keep the mathematics at the level of readers with master's-level training in statistics." (Lih-Yuan Deng, Technometrics, Vol. 46 (4), November, 2004) "The book by Thomas Santner et al. illustrates the usefulness of computer models and statistical methodologies to extract information in stimulated data ... . Computer modeling has been challenging to the practitioners, and this book eases these challenges with the exposure of basic ideas and daunting formulas. This well written book seven chapters ... . The references are exhaustive and current." (Ramalingam Shanmugam, Journal of Statistical Computation and Simulation, Vol. 75 (2), February, 2005)

Innehållsförteckning

1 Physical Experiments and Computer Experiments.- 2 Preliminaries.- 3 Predicting Output from Computer Experiments.- 4 Additional Topics in Prediction Methodology.- 5 Space-Filling Designs for Computer Experiments.- 6 Some Criterion-based Experimental Designs.- 7 Sensitivity Analysis, Validation, and Other Issues.- A List of Notation.- A.1 Abbreviations.- A.2 Symbols.- B Mathematical Facts.- B.1 The Multivariate Normal Distribution.- B.3 Some Results from Matrix Algebra.- C PErK: Parametric Empirical Kriging.- C.1 Introduction.- C.2 PErK Job File Options and Output.- C.3 Examples.- References.- Author Index.