  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.
