Analyzing Stochastic Computer Models: A Review with Opportunities

TL;DR

This review discusses statistical methods for analyzing stochastic computer models, emphasizing Gaussian process surrogates, experiment design, calibration, and open research questions, with practical examples and code.

Contribution

It provides a comprehensive overview of statistical techniques for stochastic computer models, highlighting extensions of Gaussian processes and practical implementation insights.

Findings

Gaussian process surrogates are central to stochastic model analysis

Design and calibration of stochastic experiments are key challenges

Open questions remain in extending methods for complex stochastic models

Abstract

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.