Communicating Likelihoods with Normalising Flows

We present a machine-learning-based workflow to model an unbinned likelihood from its samples. A key advancement over existing approaches is the validation of the learned likelihood using rigorous statistical tests of the joint distribution, such as the Kolmogorov-Smirnov test of the joint distribution. Our method enables the reliable communication of experimental and phenomenological likelihoods for subsequent analyses. We demonstrate its effectiveness through three case studies in high-energy physics. To support broader adoption, we provide an open-source reference implementation, nabu.

Testable Likelihoods for Beyond-the-Standard Model Fits

Studying potential BSM effects at the precision frontier requires accurate transfer of information from low-energy measurements to high-energy BSM models. We propose to use normalising flows to construct likelihood functions that achieve this transfer. Likelihood functions constructed in this way provide the means to generate additional samples and admit a ``trivial'' goodness-of-fit test in form of a $\chi^2$ test statistic. Here, we study a particular form of normalising flow, apply it to a multi-modal and non-Gaussian example, and quantify the accuracy of the likelihood function and its test statistic.