Gaussian Process regression for astronomical time-series

TL;DR

Gaussian Processes are a flexible, robust, and mathematically simple method increasingly used in astronomy to model complex time-series data, with applications spanning from exoplanets to active galactic nuclei.

Contribution

This review introduces Gaussian Processes in astronomy, discusses modeling choices, reviews applications, and provides practical examples and software resources.

Findings

GPs effectively model diverse astrophysical time-series.

Open source GP software facilitates broader adoption.

Scalability remains a challenge for large datasets.

Abstract

The last two decades have seen a major expansion in the availability, size, and precision of time-domain datasets in astronomy. Owing to their unique combination of flexibility, mathematical simplicity and comparative robustness, Gaussian Processes (GPs) have emerged recently as the solution of choice to model stochastic signals in such datasets. In this review we provide a brief introduction to the emergence of GPs in astronomy, present the underlying mathematical theory, and give practical advice considering the key modelling choices involved in GP regression. We then review applications of GPs to time-domain datasets in the astrophysical literature so far, from exoplanets to active galactic nuclei, showcasing the power and flexibility of the method. We provide worked examples using simulated data, with links to the source code, discuss the problem of computational cost and scalability, and give a snapshot of the current ecosystem of open source GP software packages. Driven by further algorithmic and conceptual advances, we expect that GPs will continue to be an important tool for robust and interpretable time domain astronomy for many years to come.