Thomas J. Santner, Brian J. Williams, William I. Notz

The Design and Analysis of Computer Experiments (eBook, PDF)

• Format: PDF

Produktbeschreibung

The computer has become an increasingly popular tool for exploring the relationship between a measured response and factors thought to affect the response. In many cases, the basis of a computer model is a mathematical theory that implicitly relates the response to the factors. A computer model becomes possible given suitable numerical methods for accurately solving the mathematical system and appropriate computer hardware and software to implement the numerical methods. For example, in many engineering applications, the relationship is described by a dynamical system and the numerical method is a finite element code. The resulting computer "simulator" can generate the response corresponding to any given set of values of the factors. This allows one to use the code to conduct a "computer experiment" to explore the relationship between the response and the factors. In some cases, computer experimentation is feasible when a properly designed physical experiment (the gold standard forestablishing cause and effect) is impossible; the number of input variables may be too large to consider performing a physical experiment, or power studies may show it is economically prohibitive to run an experiment on the scale required to answer a given research question.

This book describes methods for designing and analyzing experiments that are conducted using a computer code rather than 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. It illustrates these methods with code that is available to the reader at the companion web site for the book.

Thomas Santner has been a professor in the Department of Statistics at The Ohio State University since 1990. At Ohio State, he has served as department Chair and Director of thedepartment's Statistical Consulting Service. Previously, he was a professor in the School of Operations Research and Industrial Engineering at Cornell University. He is a Fellow of the American Statistical Association and the Institute of Mathematical Statistics, and is an elected ordinary member of the International Statistical Institute. He visited Ludwig Maximilians Universität in Munich, Germany on a Fulbright Scholarship in 1996-97.

Brian Williams has been an Associate Statistician at the RAND Corporation since 2000. His research interests include experimental design, computer experiments, Bayesian inference, spatial statistics and statistical computing. He holds a Ph.D. in statistics from The Ohio State University.

William Notz is a professor in the Department of Statistics at The Ohio State University. At Ohio State, he has served as acting department chair, associate dean of the College of Mathematical and Physical Sciences, and as director of the department's Statistical Consulting Service. He has also served as Editor of the journal Technometrics and is a Fellow of the American Statistical Association.

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Produktdetails

• Verlag: Springer New York
• Seitenzahl: 284
• Erscheinungstermin: 9. März 2013
• Englisch
• ISBN-13: 9781475737998
• Artikelnr.: 44179371

Autorenporträt

  ¿Thomas J.  Santner is Professor Emeritus in the Department of Statistics at The Ohio State University.  At Ohio State, he has served as department Chair and Director of the Department's Statistical Consulting Service. Previously, he was a professor in the School of Operations Research and Industrial Engineering at Cornell University. His research interests include the design and analysis of experiments, particularly those involving computer simulators, Bayesian inference, and the analysis of discrete response data.   He is a Fellow of the American Statistical Association, the Institute of Mathematical Statistics, the American Association for the Advancement of Science, and is an elected ordinary member of the International Statistical Institute.  He has held visiting appointments at the National Cancer Institute, the University of Washington, Ludwig Maximilians Universität (Munich, Germany), the National Institute of Statistical Science (NISS), and the Isaac Newton Institute (Cambridge, England).     Brian J. Williams has been Statistician at the Los Alamos National Laboratory RAND Corporation since 2003. His research interests include experimental design, computer experiments, Bayesian inference, spatial statistics and statistical computing. Williams was named a Fellow of the American Statistical Association in 2015 and is also the recipient of the Los Alamos Achievement Award for his leadership role in the Consortium for Advanced Simulation of Light Water Reactors (CASL) Program. He holds a doctorate in statistics from The Ohio State University.   William I.  Notz is Professor Emeritus in the Department of Statistics at The Ohio State University.  At Ohio State, he has served as acting department chair, associate dean of the College of Mathematical and Physical Sciences, and as director of the department's StatisticalConsulting Service. His research focuses on experimental designs for computer experiments and he is particularly interested in sequential strategies for selecting points at which to run a computer simulator in order to optimize some performance measure related to the objectives of the computer experiment.  A Fellow of the American Statistical Association, Notz has also served as Editor of the journals Technometrics and the  Journal of Statistics Education.

Inhaltsangabe

Physical Experiments and Computer Experiments.- Stochastic Process Models for Describing Simulator Output.- Empirical Best Linear Unbiased Prediction for Simulator Output.- Bayesian Inference for Simulator Output.- Space-Filling Designs for Computer Experiments.- Some Criterion-based Experimental Designs.- Sensitivity Analysis and Variable Screening.- Calibration.- Appendix A : List of Notation.- Appendix B: Mathematical Facts.- Appendix C: An Overview of Selected Optimization Algorithms.- Appendix D: An Introduction to Markov Chain Monte Carlo Algorithms.- Appendix E: A Primer on Constructing Quasi-Monte Carlo Sequences.

Rezensionen

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 ofcomputer 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)