Inferring correlated distributions: boosted top jets

Abstract: Improving the understanding of signal and background distributions in signal-region is a valuable key to enhance any analysis in collider physics. This is usually a difficult task because -- among others -- signal and backgrounds are hard to discriminate in signal-region, simulations may reach a limit of reliability if they need to model non-perturbative QCD, and distributions are multi-dimensional and many times may be correlated within each class. Bayesian density estimation is a technique that leverages prior knowledge and data correlations to effectively extract information from data in signal-region. In this work we extend previous works on data-driven mixture models for meaningful unsupervised signal extraction in collider physics to incorporate correlations between features. Using a standard dataset of top and QCD jets, we show how simulators, despite having an expected bias, can be used to inject sufficient inductive nuance into an inference model in terms of priors to then be corrected by data and estimate the true correlated distributions between features within each class. We compare the model with and without correlations to show how the signal extraction is sensitive to their inclusion and we quantify the improvement due to the inclusion of correlations using both supervised and unsupervised metrics.