Bayesian technique to combine independently-trained Machine-Learning models applied to direct dark matter detection

We carry out a Bayesian analysis of dark matter (DM) direct detection data to determine particle model parameters using the Truncated Marginal Neural Ratio Estimation (TMNRE) machine learning technique. TMNRE avoids an explicit calculation of the likelihood, which instead is estimated from simulated data, unlike in traditional Markov Chain Monte Carlo (MCMC) algorithms. This considerably speeds up, by several orders of magnitude, the computation of the posterior distributions, which allows to perform the Bayesian analysis of an otherwise computationally prohibitive number of benchmark points. In this article we demonstrate that, in the TMNRE framework, it is possible to include, combine, and remove different datasets in a modular fashion, which is fast and simple as there is no need to re-train the machine learning algorithm or to define a combined likelihood. In order to assess the performance of this method, we consider the case of WIMP DM with spin-dependent and independent interactions with protons and neutrons in a xenon experiment. After validating our results with MCMC, we employ the TMNRE procedure to determine the regions where the DM parameters can be reconstructed. Finally, we present CADDENA, a Python package that implements the modular Bayesian analysis of direct detection experiments described in this work.