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

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