Statistical Analysis of Complex Computer Models in Astronomy

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.

Interpolation and Synthesis of Sparse Samples in Exoplanet Atmospheric Modeling

“…The method most closely related to kriging is known as "Gaussian process emulation," "Gaussian process modeling," or "Gaussian process regression," which has also been applied to many problems in astronomy (e.g., Lukemire et al 2021). Gaussian process emulation is used as a synonym for kriging in some publications, and many of the differences between the two methods are only a choice in vocabulary (for example, the "variogram" in kriging is equivalent to the "kernel function" in Gaussian process emulation).…”

Measure or infer? Role of modeling and machine learning in modern astronomy

“…Joshua Lukemire et al [5] address the problem of time-consuming sophisticated computer simulations used by scientists to test complex systems by exploring computationally cheap surrogates to facilitate analysis and optimization of the underlying system. Their study discusses design criteria that allow astronomy researchers to extract the maximum benefit offered by Gaussian Process surrogate modeling (for exampleidentification of optimal Latin hypercube designs).…”