Bayesian analysis of multiple direct detection experiments

Bayesian methods offer a coherent and efficient framework for implementing uncertainties into induction problems. In this article, we review how this approach applies to the analysis of dark matter direct detection experiments. In particular we discuss the exclusion limit of XENON100 and the debated hints of detection under the hypothesis of a WIMP signal. Within parameter inference, marginalizing consistently over uncertainties to extract robust posterior probability distributions, we find that the claimed tension between XENON100 and the other experiments can be partially alleviated in isospin violating scenario, while elastic scattering model appears to be compatible with the frequentist statistical approach. We then move to model comparison, for which Bayesian methods are particularly well suited. Firstly, we investigate the annual modulation seen in CoGeNT data, finding that there is weak evidence for a modulation. Modulation models due to other physics compare unfavorably with the WIMP models, paying the price for their excessive complexity. Secondly, we confront several coherent scattering models to determine the current best physical scenario compatible with the experimental hints. We find that exothermic and inelastic dark matter are moderatly disfavored against the elastic scenario, while the isospin violating model has a similar evidence. Lastly the Bayes' factor gives inconclusive evidence for an incompatibility between the data sets of XENON100 and the hints of detection. The same question assessed with goodness of fit would indicate a 2 sigma discrepancy. This suggests that more data are therefore needed to settle this question.Comment: 29 pages, 8 figures; invited review for the special issue of the journal Physics of the Dark Universe; matches the published versio