February 2022 Analyzing Stochastic Computer Models: A Review with Opportunities
Evan Baker, Pierre Barbillon, Arindam Fadikar, Robert B. Gramacy, Radu Herbei, David Higdon, Jiangeng Huang, Leah R. Johnson, Pulong Ma, Anirban Mondal, Bianica Pires, Jerome Sacks, Vadim Sokolov
Author Affiliations +
Statist. Sci. 37(1): 64-89 (February 2022). DOI: 10.1214/21-STS822


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.

Funding Statement

We also gratefully acknowledge the support and funding provided by SAMSI during the Model Uncertainty: Mathematical and Statistical program, 2018–19.
Pierre Barbillon received support from the Marie-Curie FP7 COFUND People Programme of the European Union, through the award of an AgreenSkills/ AgreenSkills+ fellowship (under grant agreement n∘609398).
Robert Gramacy and Dave Higdon were supported in part by DOE LAB 17-1697 via a subaward from Argonne National Laboratory for SciDAC/DOE Office of Science ASCR and High Energy Physics. They were also supported by the National Science Foundation. Gramacy under Grant DMS-1821258; Higdon under Grant CCF-1918770.
Leah R Johnson was partially supported by NSF DMS/ DEB #1750113.
Pulong Ma’s research was partly supported by the postdoctoral fellowship funded by the National Science Foundation under Grant DMS-1638521 to SAMSI.


We thank the review team for their constructive comments during the review process.

Moreover, Professor David Banks, Director of SAMSI, is thanked for suggesting and encouraging the writing of this review.

Any opinions, findings and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.

Bianica Pires’ affiliation with The MITRE Corporation is provided for identification purposes only and is not intended to convey or imply MITRE’s concurrence with, or support for, the positions, opinions, or viewpoints expressed by the author.


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Evan Baker. Pierre Barbillon. Arindam Fadikar. Robert B. Gramacy. Radu Herbei. David Higdon. Jiangeng Huang. Leah R. Johnson. Pulong Ma. Anirban Mondal. Bianica Pires. Jerome Sacks. Vadim Sokolov. "Analyzing Stochastic Computer Models: A Review with Opportunities." Statist. Sci. 37 (1) 64 - 89, February 2022. https://doi.org/10.1214/21-STS822


Published: February 2022
First available in Project Euclid: 19 January 2022

MathSciNet: MR4371096
zbMATH: 07474198
Digital Object Identifier: 10.1214/21-STS822

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

Rights: Copyright © 2022 Institute of Mathematical Statistics


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Vol.37 • No. 1 • February 2022
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