Surrogates: Gaussian Process Modeling, Design, and Optimization for the Applied Sciences

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.

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.