Treatment of systematic uncertainties with Bayesian networks

Abstract

We show an innovative approach based on Bayesian networks and linear algebra providing a solid and complete solution to the problem of the detector response and the related systematic effects. As a case study, we consider the dark matter direct detection searches. In this context, it is crucial to develop a reliable analysis framework, which is able to take into account all the relevant systematic effects in a clean and accessible way. The relations connecting the calibration parameters of the experiment to the final observed data spectrum are characterized by substantial complexity and non linearity. Usual approaches to direct detection data analysis involve multi-templates techniques. By means of our technique however it is possible to represent the full detector response to any background/signal event keeping the dependence on the detector parameters explicit. The advantage of this kind of approach is twofold: from the statistical point of view it is a solid and rigorous way to perform the analysis; from the computational point of view, we demonstrate that it is possible to represent the response of the detector by a set of matrices, allowing to use a GPU accelerated analysis code to improve the performance of the fit.