Annual modulations from secular variations: not relaxing DAMA?

In a recent paper [arXiv:2002.00459], Buttazzo et al. show how the annually modulated rate of the DAMA experiments can be possibly interpreted as an artefact due to the interplay between a time-dependent background and the method to account for it. In this work, we compare this hypothesis against the sinusoidal dark matter signal as proposed by the DAMA collaboration. We produce in a Bayesian approach a quantitative comparison of how much the experimental observations are in support of each hypothesis. Our conclusions are that the odds against the hypothesis of a time varying background being responsible for the annual modulation are decreased by a Bayes factor larger than 10^8 after considering the public available data of the DAMA/NaI and DAMA/LIBRA experiments. In this work we also elaborate on general aspects of the analysis procedure. Indeed, in order to optimise the background subtraction procedure, the DAMA collaboration only considers data-taking cycles with a duration of roughly one year. We argue that any data-taking cycle is informative, and we propose a procedure to include this effect, as well as the possibility to include a slowly varying component for the background.