BGLS: A Bayesian formalism for the generalised LombScargle periodogram
Abstract
Context. Frequency analyses are very important in astronomy today, not least in the evergrowing field of exoplanets, where shortperiod 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 LombScargle periodogram (BGLS), we can easily recover the expression for the nonBayesian version. In the simulated examples we show that this new formalism recovers the underlying periods better than previous versions. A Pythonbased code is available for the community.
https://www.astro.up.pt/exoearths/tools.html A copy of the code is only available at the CDS via anonymous ftp to http://cdsarc.ustrasbg.fr (ftp://130.79.128.5) or via http://cdsarc.ustrasbg.fr/vizbin/qcat?J/A+A/573/A101
 Publication:

Astronomy and Astrophysics
 Pub Date:
 January 2015
 DOI:
 10.1051/00046361/201424908
 arXiv:
 arXiv:1412.0467
 Bibcode:
 2015A&A...573A.101M
 Keywords:

 methods: data analysis;
 methods: statistical;
 Astrophysics  Instrumentation and Methods for Astrophysics;
 Astrophysics  Earth and Planetary Astrophysics
 EPrint:
 6 pages, 6 figures, accepted for publication in A&