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E-raamat: Design and Analysis of Computer Experiments

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  • Formaat: PDF+DRM
  • Sari: Springer Series in Statistics
  • Ilmumisaeg: 08-Jan-2019
  • Kirjastus: Springer-Verlag New York Inc.
  • Keel: eng
  • ISBN-13: 9781493988471
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Design and Analysis of Computer ExperimentsSuurem pilt
  • Formaat: PDF+DRM
  • Sari: Springer Series in Statistics
  • Ilmumisaeg: 08-Jan-2019
  • Kirjastus: Springer-Verlag New York Inc.
  • Keel: eng
  • ISBN-13: 9781493988471
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This book describes methods for designing and analyzing experiments that are conducted using a computer code, a computer experiment, and, when possible, a physical experiment. Computer experiments continue to increase in popularity as surrogates for and adjuncts to physical experiments. Since the publication of the first edition, there have been many methodological advances and software developments to implement these new methodologies. The computer experiments literature has emphasized the construction of algorithms for various data analysis tasks (design construction, prediction, sensitivity analysis, calibration among others), and the development of web-based repositories of designs for immediate application. While it is written at a level that is accessible to readers with Masters-level training in Statistics, the book is written in sufficient detail to be useful for practitioners and researchers.

 

New to this revised and expanded edition:

• An expanded presentation of basic material on computer experiments and Gaussian processes with additional simulations and examples     

• A new comparison of plug-in prediction methodologies for real-valued simulator output

• An enlarged discussion of space-filling designs including Latin Hypercube designs (LHDs), near-orthogonal designs, and nonrectangular regions

• A chapter length description of process-based designs for optimization, to improve good overall fit, quantile estimation, and Pareto optimization

• A new chapter describing graphical and numerical sensitivity analysis tools

• Substantial new material on calibration-based prediction and inference for calibration parameters

•  Lists of software that can be used to fit models discussed in the book to aid practitioners 

1 Physical Experiments and Computer Experiments
1(26)
1.1 Introduction
1(2)
1.2 Examples of Computer Simulator Models
3(17)
1.3 Some Common Types of Computer Experiments
20(5)
1.3.1 Homogeneous-Input Simulators
21(1)
1.3.2 Mixed-Input Simulators
22(2)
1.3.3 Multiple Outputs
24(1)
1.4 Organization of the Remainder of the Book
25(2)
2 Stochastic Process Models for Describing Computer Simulator Output
27(40)
2.1 Introduction
27(3)
2.2 Gaussian Process Models for Real-Valued Output
30(13)
2.2.1 Introduction
30(4)
2.2.2 Some Correlation Functions for GP Models
34(7)
2.2.3 Using the Correlation Function to Specify a GP with Given Smoothness Properties
41(2)
2.3 Increasing the Flexibility of the GP Model
43(6)
2.3.1 Hierarchical GP Models
46(2)
2.3.2 Other Nonstationary Models
48(1)
2.4 Models for Output Having Mixed Qualitative and Quantitative Inputs
49(8)
2.5 Models for Multivariate and Functional Simulator Output
57(8)
2.5.1 Introduction
57(2)
2.5.2 Modeling Multiple Outputs
59(3)
2.5.3 Other Constructive Models
62(1)
2.5.4 Models for Simulators Having Functional Output
63(2)
2.6
Chapter Notes
65(2)
3 Empirical Best Linear Unbiased Prediction of Computer Simulator Output
67(48)
3.1 Introduction
67(1)
3.2 BLUP and Minimum MSPE Predictors
68(8)
3.2.1 Best Linear Unbiased Predictors
68(2)
3.2.2 Best MSPE Predictors
70(5)
3.2.3 Some Properties of y(xte)
75(1)
3.3 Empirical Best Linear Unbiased Prediction of Univariate Simulator Output
76(8)
3.3.1 Introduction
76(1)
3.3.2 Maximum Likelihood EBLUPs
77(1)
3.3.3 Restricted Maximum Likelihood EBLUPs
78(1)
3.3.4 Cross-Validation EBLUPs
79(1)
3.3.5 Posterior Mode EBLUPs
80(1)
3.3.6 Examples
80(4)
3.4 A Simulation Comparison of EBLUPs
84(11)
3.4.1 Introduction
84(1)
3.4.2 A Selective Review of Previous Studies
85(3)
3.4.3 A Complementary Simulation Study of Prediction Accuracy and Prediction Interval Accuracy
88(7)
3.4.4 Recommendations
95(1)
3.5 EBLUP Prediction of Multivariate Simulator Output
95(12)
3.5.1 Optimal Predictors for Multiple Outputs
96(2)
3.5.2 Examples
98(9)
3.6
Chapter Notes
107(8)
3.6.1 Proof That (3.2.7) Is a BLUP
107(2)
3.6.2 Derivation of Formula 3.2.8
109(1)
3.6.3 Implementation Issues
109(3)
3.6.4 Software for Computing EBLUPs
112(1)
3.6.5 Alternatives to Kriging Metamodels and Other Topics
113(2)
4 Bayesian Inference for Simulator Output
115(30)
4.1 Introduction
115(2)
4.2 Inference for Conjugate Bayesian Models
117(11)
4.2.1 Posterior Inference for Model (4.1.1) When v = β
117(6)
4.2.2 Posterior Inference for Model (4.1.1) When v = (β, λz)
123(5)
4.3 Inference for Non-conjugate Bayesian Models
128(8)
4.3.1 The Hierarchical Bayesian Model and Posterior
129(3)
4.3.2 Predicting Failure Depths of Sheet Metal Pockets
132(4)
4.4
Chapter Notes
136(9)
4.4.1 Outline of the Proofs of Theorems 4.1 and 4.2
136(6)
4.4.2 Eliciting Priors for Bayesian Regression
142(1)
4.4.3 Alternative Sampling Algorithms
142(1)
4.4.4 Software for Computing Bayesian Predictions
142(3)
5 Space-Filling Designs for Computer Experiments
145(56)
5.1 Introduction
145(5)
5.1.1 Some Basic Principles of Experimental Design
145(3)
5.1.2 Design Strategies for Computer Experiments
148(2)
5.2 Designs Based on Methods for Selecting Random Samples
150(10)
5.2.1 Designs Generated by Elementary Methods for Selecting Samples
151(1)
5.2.2 Designs Generated by Latin Hypercube Sampling
152(5)
5.2.3 Some Properties of Sampling-Based Designs
157(3)
5.3 Latin Hypercube Designs with Additional Properties
160(12)
5.3.1 Latin Hypercube Designs Whose Projections Are Space-Filling
160(4)
5.3.2 Cascading, Nested, and Sliced Latin Hypercube Designs
164(3)
5.3.3 Orthogonal Latin Hypercube Designs
167(3)
5.3.4 Symmetric Latin Hypercube Designs
170(2)
5.4 Designs Based on Measures of Distance
172(9)
5.5 Distance-Based Designs for Non-rectangular Regions
181(3)
5.6 Other Space-Filling Designs
184(7)
5.6.1 Designs Obtained from Quasi-Random Sequences
184(2)
5.6.2 Uniform Designs
186(5)
5.7
Chapter Notes
191(10)
5.7.1 Proof That TL is Unbiased and of the Second Part of Theorem 5.1
191(5)
5.7.2 The Use of LHDs in a Regression Setting
196(1)
5.7.3 Other Space-Filling Designs
197(1)
5.7.4 Software for Constructing Space-Filling Designs
198(2)
5.7.5 Online Catalogs of Designs
200(1)
6 Some Criterion-Based Experimental Designs
201(46)
6.1 Introduction
201(1)
6.2 Designs Based on Entropy and Mean Squared Prediction Error Criterion
202(10)
6.2.1 Maximum Entropy Designs
202(4)
6.2.2 Mean Squared Prediction Error Designs
206(6)
6.3 Designs Based on Optimization Criteria
212(24)
6.3.1 Introduction
212(1)
6.3.2 Heuristic Global Approximation
213(1)
6.3.3 Mockus Criteria Optimization
214(2)
6.3.4 Expected Improvement Algorithms for Optimization
216(9)
6.3.5 Constrained Global Optimization
225(4)
6.3.6 Pareto Optimization
229(7)
6.4 Other Improvement Criterion-Based Designs
236(6)
6.4.1 Introduction
236(1)
6.4.2 Contour Estimation
237(1)
6.4.3 Percentile Estimation
238(3)
6.4.4 Global Fit
241(1)
6.5
Chapter Notes
242(5)
6.5.1 The Hypervolume Indicator for Approximations to Pareto Fronts
243(1)
6.5.2 Other MSPE-Based Optimal Designs
244(1)
6.5.3 Software for Constructing Criterion-Based Designs
245(2)
7 Sensitivity Analysis and Variable Screening
247(52)
7.1 Introduction
247(2)
7.2 Classical Approaches to Sensitivity Analysis
249(3)
7.2.1 Sensitivity Analysis Based on Scatterplots and Correlations
249(1)
7.2.2 Sensitivity Analysis Based on Regression Modeling
249(3)
7.3 Sensitivity Analysis Based on Elementary Effects
252(7)
7.4 Global Sensitivity Analysis
259(15)
7.4.1 Main Effect and Joint Effect Functions
259(5)
7.4.2 A Functional ANOVA Decomposition
264(3)
7.4.3 Global Sensitivity Indices
267(7)
7.5 Estimating Effect Plots and Global Sensitivity Indices
274(12)
7.5.1 Estimating Effect Plots
275(7)
7.5.2 Estimating Global Sensitivity Indices
282(4)
7.6 Variable Selection
286(5)
7.7
Chapter Notes
291(8)
7.7.1 Designing Computer Experiments for Sensitivity Analysis
291(1)
7.7.2 Orthogonality of Sobol' Terms
292(1)
7.7.3 Weight Functions g(x) with Nonindependent Components
293(1)
7.7.4 Designs for Estimating Elementary Effects
294(1)
7.7.5 Variable Selection
294(1)
7.7.6 Global Sensitivity Indices for Functional Output
294(3)
7.7.7 Software
297(2)
8 Calibration
299(108)
8.1 Introduction
299(2)
8.2 The Kennedy and O'Hagan Calibration Model
301(6)
8.2.1 Introduction
301(1)
8.2.2 The KOH Model
301(6)
8.3 Calibration with Univariate Data
307(14)
8.3.1 Bayesian Inference for the Calibration Parameter θ
308(1)
8.3.2 Bayesian Inference for the Mean Response μ(x) of the Physical System
308(1)
8.3.3 Bayesian Inference for the Bias δ(x) and Calibrated Simulator E[ Ys(x, θ)|y]
309(12)
8.4 Calibration with Functional Data
321(25)
8.4.1 The Simulation Data
322(5)
8.4.2 The Experimental Data
327(7)
8.4.3 Joint Statistical Models and Log Likelihood Functions
334(12)
8.5 Bayesian Analysis
346(26)
8.5.1 Prior and Posterior Distributions
346(12)
8.5.2 Prediction
358(14)
8.6
Chapter Notes
372(9)
8.6.1 Special Cases of Functional Emulation and Prediction
372(2)
8.6.2 Some Other Perspectives on Emulation and Calibration
374(4)
8.6.3 Software for Calibration and Validation
378(3)
A List of Notation
381(4)
A.1 Abbreviations
381(1)
A.2 Symbols
382(3)
B Mathematical Facts
385(8)
B.1 The Multivariate Normal Distribution
385(2)
B.2 The Gamma Distribution
387(1)
B.3 The Beta Distribution
388(1)
B.4 The Non-central Student t Distribution
388(1)
B.5 Some Results from Matrix Algebra
389(4)
C An Overview of Selected Optimization Algorithms
393(8)
C.1 Newton/Quasi-Newton Algorithms
394(1)
C.2 Direct Search Algorithms
395(1)
C.2.1 Nelder--Mead Simplex Algorithm
395(1)
C.2.2 Generalized Pattern Search and Surrogate Management Framework Algorithms
396(2)
C.2.3 DIRECT Algorithm
398(1)
C.3 Genetic/Evolutionary Algorithms
398(1)
C.3.1 Simulated Annealing
398(1)
C.3.2 Particle Swarm Optimization
399(2)
D An Introduction to Markov Chain Monte Carlo Algorithms
401(4)
E A Primer on Constructing Quasi-Monte Carlo Sequences
405(2)
References 407(18)
Author Index 425(6)
Subject Index 431
 





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.
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