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.

In modern science, deterministic computer models are often used to understand complex phenomena, and a thriving statistical community has grown around effectively analysing 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 and results of various methods.

No abstract

Abstract. Land surface models are typically integrated into global climate projections, but as their spatial resolution increases the prospect of using them to aid in local policy decisions becomes more appealing. If these complex models are to be used to make local decisions, then a full quantification of uncertainty is necessary, but the computational cost of running just one full simulation at high resolution can hinder proper analysis. Statistical emulation is an increasingly common technique for developing fast approximate models in a way that maintains accuracy but also provides comprehensive uncertainty bounds for the approximation. In this work, we developed a statistical emulation framework for land surface models, enabling fast predictions at a high resolution. To do so, our emulation framework acknowledges, and makes use of, the multitude of contextual data that are often fed into land surface models (sometimes called forcing data, or driving data), such as air temperature or various soil properties. We use The Joint UK Land Environment Simulator (JULES) as a case study for this methodology, and perform initial sensitivity analysis and parameter tuning to showcase its capabilities. The JULES is perhaps one of the most complex land surface models and so our success here suggests incredible gains can be made for all types of land surface model.

The analysis of computer models can be aided by the construction of surrogate models, or emulators, that statistically model the numerical computer model. Increasingly, computer models are becoming stochastic, yielding different outputs each time they are run, even if the same input values are used. Stochastic computer models are more difficult to analyse and more difficult to emulate -often requiring substantially more computer model runs to fit. We present a method of using deterministic approximations of the computer model to better construct an emulator. The method is applied to numerous toy examples, as well as an idealistic epidemiology model, and a model from the building performance field.