BGLS: A Bayesian formalism for the generalised Lomb-Scargle periodogram

TL;DR

This paper introduces a Bayesian formalism for the Lomb-Scargle periodogram, improving frequency detection accuracy in astronomical data analysis by incorporating weights and offsets, with a practical Python implementation.

Contribution

It presents a new Bayesian generalised Lomb-Scargle periodogram formalism that enhances frequency analysis in astronomy, including weights and offsets, with an accessible implementation.

Findings

Better recovery of underlying periods in simulations

Formalism aligns with non-Bayesian Lomb-Scargle when simplified

Provides a practical Python code for community use

Abstract

Context. Frequency analyses are very important in astronomy today, not least in the ever-growing field of exoplanets, where short-period signals in stellar radial velocity data are investigated. Periodograms are the main (and powerful) tools for this purpose. However, recovering the correct frequencies and assessing the probability of each frequency is not straightforward. Aims. We provide a formalism that is easy to implement in a code, to describe a Bayesian periodogram that includes weights and a constant offset in the data. The relative probability between peaks can be easily calculated with this formalism. We discuss the differences and agreements between the various periodogram formalisms with simulated examples. Methods. We used the Bayesian probability theory to describe the probability that a full sine function (including weights derived from the errors on the data values and a constant offset) with a specific frequency is present in the data. Results. From the expression for our Baysian generalised Lomb-Scargle periodogram (BGLS), we can easily recover the expression for the non-Bayesian version. In the simulated examples we show that this new formalism recovers the underlying periods better than previous versions. A Python-based code is available for the community.