Approximate Differentiable Likelihoods for Astroparticle Physics Experiments

Abstract: Traditionally, inference in liquid xenon direct detection dark matter experiments has used estimators of event energy or density estimation of simulated data. Such methods have drawbacks compared to the computation of explicit likelihoods, such as an inability to conduct statistical inference in high-dimensional parameter spaces, or a failure to make use of all available information. In this work, we implement a continuous approximation of an event simulator model within a probabilistic programming framework, allowing for the application of high performance gradient-based inference methods such as the No-U-Turn Sampler. We demonstrate an improvement in inference results, with percent-level decreases in measurement uncertainties. Finally, in the case where some observables can be measured using multiple independent channels, such a method also enables the incorporation of additional information seamlessly, allowing for full use of the available information to be made.