Statistical Analysis of Complex Computer Models in Astronomy

TL;DR

This paper discusses statistical methods for building efficient Gaussian process emulators of complex computer models, emphasizing design strategies for input selection and their applications in astronomy research.

Contribution

It introduces methods for constructing space-filling designs and fitting Gaussian process models specifically tailored for astronomical computer experiments.

Findings

Effective space-filling design strategies for input selection.

Gaussian process models accurately emulate complex simulations.

Applications demonstrated in astronomy research contexts.

Abstract

We introduce statistical techniques required to handle complex computer models with potential applications to astronomy. Computer experiments play a critical role in almost all fields of scientific research and engineering. These computer experiments, or simulators, are often computationally expensive, leading to the use of emulators for rapidly approximating the outcome of the experiment. Gaussian process models, also known as Kriging, are the most common choice of emulator. While emulators offer significant improvements in computation over computer simulators, they require a selection of inputs along with the corresponding outputs of the computer experiment to function well. Thus, it is important to select inputs judiciously for the full computer simulation to construct an accurate emulator. Space-filling designs are efficient when the general response surface of the outcome is unknown, and thus they are a popular choice when selecting simulator inputs for building an emulator. In this tutorial we discuss how to construct these space filling designs, perform the subsequent fitting of the Gaussian process surrogates, and briefly indicate their potential applications to astronomy research.