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.
- 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
1 Historical Perspective
2 Four Motivating Datasets
3 Steepest Ascent and Ridge Analysis
4 Space-filling Design
5 Gaussian process regression
6 Model-Based Design for GPs
8 Calibration and Sensitivity
9 GP Fidelity and Scale
Appendix A Numerical Linear Algebra for Fast GPs
Appendix B An Experiment Game
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.
"The coverage of this book is unique and important. It focuses on a current area at the edge of applied mathematics and statistics, a domain that really should be substantially better-developed. For researchers and students who already have a solid foundation in statistics and familiarity with R, and want to know more about how statistics can be used in the approximation of complex functions and numerical optimization (i.e. computer experiments), this should be a welcome resource."
-Max Morris, Iowa State University, USA
“This book is a fantastic exploration of Gaussian process surrogates and a variety of applications to which they have been utilized. This approach is rapidly expanding in both the statistical and machine learning communities. I particularly enjoyed the applied focus of this book and the ease with which the author enables the reader to “follow along”, by providing code for each example discussed. In my view, the technical content of the book is well-chosen, and the flow of material should be very well-received by the readership.”
-Brian J. Williams, Scientist, Los Alamos National Laboratory