  We study the problem of periodicity detection in massive data sets of
photometric or radial velocity time series, as presented by ESA's Gaia mission.
Periodicity detection hinges on the estimation of the false alarm probability
(FAP) of the extremum of the periodogram of the time series. We consider the
problem of its estimation with two main issues in mind. First, for a given
number of observations and signal-to-noise ratio, the rate of correct
periodicity detections should be constant for all realized cadences of
observations regardless of the observational time patterns, in order to avoid
sky biases that are difficult to assess. Second, the computational loads should
be kept feasible even for millions of time series. Using the Gaia case, we
compare the $F^M$ method (Paltani 2004, Schwarzenberg-Czerny 2012), the Baluev
method (Baluev 2008) and the GEV method (S\"uveges 2014), as well as a method
for the direct estimation of a threshold. Three methods involve some unknown
parameters, which are obtained by fitting a regression-type predictive model
using easily obtainable covariates derived from observational time series. We
conclude that the GEV and the Baluev methods both provide good solutions to the
issues posed by a large-scale processing. The first of these yields the best
scientific quality at the price of some moderately costly pre-processing. When
this pre-processing is impossible for some reason (e.g. the computational costs
are prohibitive or good regression models cannot be constructed), the Baluev
method provides a computationally inexpensive alternative with slight biases in
regions where time samplings exhibit strong aliases.
