Gaussian Process Regression for Astronomical Time Series

Abstract

The past two decades have seen a major expansion in the availability, size, and precision of time-domain data sets 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 data sets. 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 modeling choices involved in GP regression. We then review applications of GPs to time-domain data sets 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. In summary: ▪ GP regression is a conceptually simple but statistically principled and powerful tool for the analysis of astronomical time series. ▪ It is already widely used in some subfields, such as exoplanets, and gaining traction in many others, such as optical transients. ▪ 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. Expected final online publication date for the Annual Review of Astronomy and Astrophysics, Volume 61 is August 2023. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

The TESS-Keck Survey. XII. A Dense 1.8 R ⊕ Ultra-short-period Planet Possibly Clinging to a High-mean-molecular-weight Atmosphere after the First Gigayear

“…The effect of a starspot on photometry is to reduce the observed (integrated) intensity when on the visible hemisphere. The net effect of many spots is quasiperiodic variability that can be treated as time-correlated noise (Haywood et al 2014;Rajpaul et al 2015;Aigrain & Foreman-Mackey 2023). The TESS photometry of TOI-1347 shows strong rotational variability with maxima/minima occurring roughly every ∼8 days (see the top panel in Figure 3).…”

In This Day and Age: An Empirical Gyrochronology Relation for Partially and Fully Convective Single Field Stars

“…Typically, a GP regressor is composed of a mean function (m; Equation (1)), which is ideally physically motivated, and a covariance function (k; Equation (2)) that captures the details that the mean function has missed. For a more detailed review of GP and its applications in astronomy, we direct the readers to Aigrain & Foreman-Mackey (2023). In this paper, we used the PYTHON package tinygp (Foreman-Mackey 2023) to construct our GP model.…”

The Epoch of Giant Planet Migration Planet Search Program. II. A Young Hot Jupiter Candidate around the AB Dor Member HS Psc*

“…Altogether we find that a joint GP model better predicts the HPF RVs compared to a Keplerian-only model. However, GP regression can be susceptible to overfitting (e.g., Aigrain & Foreman-Mackey 2023;Blunt et al 2023), leading to systematic biases that affect the interpretation of a planetary signal. This is particularly true for young systems where stellar activity signals are large.…”