Surrogates: Gaussian Process Modeling, Design, and Optimization for the Applied Sciences, 1st Edition (Hardback) book cover

Surrogates

Gaussian Process Modeling, Design, and Optimization for the Applied Sciences, 1st Edition

By Robert B. Gramacy

Chapman and Hall/CRC

545 pages | 204 Color Illus.

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Hardback: 9780367415426
pub: 2020-01-02
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Description

Surrogates: a graduate textbook, or professional handbook, on topics at the interface between machine learning, spatial statistics, computer simulation, meta-modeling (i.e., emulation), design of experiments, and optimization. Experimentation through simulation, "human out-of-the-loop" statistical support (focusing on the science), management of dynamic processes, online and real-time analysis, automation, and practical application are at the forefront.

Topics include:

  • Gaussian process (GP) regression for flexible nonparametric and nonlinear modeling.
  • Applications to uncertainty quantification, sensitivity analysis, calibration of computer models to field data, sequential design/active learning and (blackbox/Bayesian) optimization under uncertainty.
  • Advanced topics include treed partitioning, local GP approximation, modeling of simulation experiments (e.g., agent-based models) with coupled nonlinear mean and variance (heteroskedastic) models.
  • Treatment appreciates historical response surface methodology (RSM) and canonical examples, but emphasizes contemporary methods and implementation in R at modern scale.
  • Rmarkdown facilitates a fully reproducible tour, complete with motivation from, application to, and illustration with, compelling real-data examples.

Presentation targets numerically competent practitioners in engineering, physical, and biological sciences. Writing is statistical in form, but the subjects are not about statistics. Rather, they’re about prediction and synthesis under uncertainty; about visualization and information, design and decision making, computing and clean code.

Table of Contents

Preface

1 Historical Perspective

1.1 Response surface methodology

1.2 Computer experiments

1.3 A road map

1.4 Homework exercises

2 Four Motivating Datasets 31

2.1 Rocket booster dynamics

2.2 Radiative shock hydrodynamics

2.3 Predicting satellite drag

2.4 Groundwater remediation

2.5 Data out there

2.6 Homework exercises

3 Steepest Ascent and Ridge Analysis

3.1 Path of steepest ascent

3.2 Second-order response surfaces

3.3 Homework exercises

4 Space-filling Design

4.1 Latin hypercube sample

4.2 Maximin designs

4.3 Libraries and hybrids

4.4 Homework exercises

5 Gaussian process regression

5.1 Gaussian process prior

5.2 GP hyperparameters

5.3 Some interpretation and perspective

5.4 Challenges & remedies

5.5 Homework exercises

6 Model-Based Design for GPs

6.1 Model-based design

6.2 Sequential design/active learning

6.3 Fast GP updates

6.4 Homework exercises

7 Optimization

7.1 Surrogate-assisted optimization

7.2 Expected improvement

7.3 Optimization under constraints

7.4 Homework exercises

8 Calibration and Sensitivity

8.1 Calibration

8.2 Sensitivity analysis

8.3 Homework exercises

9 GP Fidelity and Scale

9.1 Compactly supported kernels

9.2 Partition models and regression trees

9.3 Local approximate GPs

9.4 Homework exercises

10 Heteroskedasticity

10.1 Replication and stochastic kriging

10.2 Coupled mean and variance GPs

10.3 Sequential design

10.4 Homework exercises

Appendix

A Numerical Linear Algebra for Fast GPs 501

A.1 Intel MKL and OSX Accelerate

A.2 Stochastic approximation

B An Experiment Game

B.1 A shiny update to an old game

B.2 Benchmarking play in real-time

Bibliography

Index

About the Author

Robert B. Gramacy is a professor of Statistics in the College of Science at Virginia Tech. Research interests include Bayesian modeling methodology, statistical computing, Monte Carlo inference, nonparametric regression, sequential design, and optimization under uncertainty. Bobby enjoys cycling and ice hockey, and watching his kids grow up too fast.

About the Series

Chapman & Hall/CRC Texts in Statistical Science

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Subject Categories

BISAC Subject Codes/Headings:
MAT029000
MATHEMATICS / Probability & Statistics / General
MAT029020
MATHEMATICS / Probability & Statistics / Multivariate Analysis
MAT029030
MATHEMATICS / Probability & Statistics / Regression Analysis