The Bayesian Generalized Lomb-Scargle periodogram (BGLS) was introduced by Mortier et al.¹ It extends the Generalized Lomb-Scargle periodogram with Bayesian probability theory. With classical periodograms, the height of a peak is expressed in an arbitrary “power”, which makes it difficult to judge how much more significant one peak is than another. BGLS instead expresses the probability that a signal with a given period is present in the data, so the relative probability of two peaks can be compared directly. BGLS is particularly useful for unevenly spaced data sets in which a classical periodogram shows several peaks of similar height, for example a true period and its 1-day alias.


For each trial frequency, BGLS fits a sinusoid plus a constant offset to the observations, weighting each observation by 1/σ², with σ its magnitude error. Rather than looking only at the best-fitting amplitude and phase, BGLS integrates over all possible amplitudes, phases and offsets. This yields the probability of that trial frequency given the data. The process is repeated for each next trial frequency.


Peranso normalizes the result so that the most probable frequency has a value of 1. All other values are probabilities relative to this best peak: a peak with a value of 0.01 is 100 times less probable than the highest peak.


Note that BGLS needs realistic magnitude errors. If no magnitude errors are available, Peranso estimates a common error from the scatter between consecutive observations. If only some observations have an error, the missing errors are replaced by the median of the available ones. With realistic errors, BGLS typically produces one very sharp peak, and the rest of the periodogram is practically zero. This is expected behaviour: the probability of all other periods is many orders of magnitude lower.


Also note that BGLS assumes a sinusoidal signal. It works very well for pulsating stars, rotational variables and superhumps, but less well for strongly non-sinusoidal light curves such as those of eclipsing binaries with narrow eclipses. For such stars it may find a harmonic (e.g. P/2 or P/3) of the true period P. Like Lomb-Scargle and GLS, BGLS may also fail to detect the correct frequencies when several periods of similar amplitude are present.


The BGLS dialog box is similar to the Lomb-Scargle dialog box. No additional parameters need to be entered.


Prominent periods of the Period Window appear as peaks.


(1) Mortier, A., Faria, J.P., Correia, C.M., Santerne, A., Santos, N.C., 2015, Astron. Astrophys., 573, A101