Probality Matching Priors in LHC Physics

Abstract

Abstract Probability matching priors (PMPs) provide a bridge between Bayesian and frequentist inference by yielding Bayesian posterior intervals with frequentist validity. PMPs are, in general, challenging to implement as they are defined as solutions to a potentially high-dimensional and non-linear PDE. Outside the orthogonal case, no general framework exists for the implementation of PMPs. Recent work has made progress in this area, although no approach can yet be applied in generality. We consider PMPs for the three Poisson system arising in LHC experiments. Connections to reference and reverse reference priors are also considered. Theoretical and simulation results are presented, with comparison to other Bayesian techniques.