Analyzing Stochastic Computer Models: A Review with Opportunities

Evan Baker (1) , Pierre M Barbillon (2) , Arindam Fadikar (3) , Robert Gramacy (4) , Radu Herbei (5) , David Higdon (5) , Jiangeng Huang (6) , Leah Johnson (4) , Pulong Ma (7) , Anirban Mondal (8) , Bianica Pires (9) , Jerome Sacks , Vadim Sokolov (10)

1 University of Exeter
2 MIA Paris-Saclay - Mathématiques et Informatique Appliquées
3 ANL - Argonne National Laboratory [Lemont]
4 Virginia Tech [Blacksburg]
5 The Ohio State University Press
6 Genentech, Inc.
7 Duke University [Durham]
8 Case Western Reserve University [Cleveland]
9 The MITRE corporation
10 George Mason University [Fairfax]

In modern science, computer models are often used to understand complex phenomena and a thriving statistical community has grown around analyzing them. This review aims to bring a spotlight to the growing prevalence of stochastic computer models—providing a catalogue of statistical methods for practitioners, an introductory view for statisticians (whether familiar with deterministic computer models or not), and an emphasis on open questions of relevance to practitioners and statisticians. Gaussian process surrogate models take center stage in this review, and these, along with several extensions needed for stochastic settings, are explained. The basic issues of designing a stochastic computer experiment and calibrating a stochastic computer model are prominent in the discussion. Instructive examples, with data and code, are used to describe the implementation of, and results from, various methods.

Keywords: agent based model; Calibration; computer experiment; computer model; Emulator; Gaussian process; surrogates; uncertainty quantification

Domains: Statistics [stat]

Evan Baker, Pierre M Barbillon, Arindam Fadikar, Robert Gramacy, Radu Herbei, et al.. Analyzing Stochastic Computer Models: A Review with Opportunities. Statistical Science, 2022, 37 (1), pp.64-89. ⟨10.1214/21-STS822⟩. ⟨hal-03566688⟩