Linear models for systematics and nuisances

TL;DR

This paper presents a linear modeling approach with Gaussian priors for effectively marginalizing systematics in astronomical data, demonstrated on K2 time-series data affected by spacecraft motion and variability.

Contribution

It introduces a linear algebra-based marginalization technique for Gaussian priors on systematic models, enabling efficient removal of systematics in astronomical time-series analysis.

Findings

Effective modeling of spacecraft motion systematics in K2 data

Fast linear algebra operations for marginalizing nuisance parameters

Improved signal recovery in noisy astronomical observations

Abstract

The target of many astronomical studies is the recovery of tiny astrophysical signals living in a sea of uninteresting (but usually dominant) noise. In many contexts (i.e., stellar time-series, or high-contrast imaging, or stellar spectroscopy), there are structured components in this noise caused by systematic effects in the astronomical source, the atmosphere, the telescope, or the detector. More often than not, evaluation of the true physical model for these nuisances is computationally intractable and dependent on too many (unknown) parameters to allow rigorous probabilistic inference. Sometimes, housekeeping data---and often the science data themselves---can be used as predictors of the systematic noise. Linear combinations of simple functions of these predictors are often used as computationally tractable models that can capture the nuisances. These models can be used to fit and subtract systematics prior to investigation of the signals of interest, or they can be used in a simultaneous fit of the systematics and the signals. In this Note, we show that if a Gaussian prior is placed on the weights of the linear components, the weights can be marginalized out with an operation in pure linear algebra, which can (often) be made fast. We illustrate this model by demonstrating the applicability of a linear model for the non-linear systematics in K2 time-series data, where the dominant noise source for many stars is spacecraft motion and variability.