Computing Likelihood Functions for High-Energy Physics Experiments when Distributions are Defined by Simulators with Nuisance Parameters

Abstract

When searching for new phenomena in high-energy physics, statistical analysis is complicated by the presence of nuisance parameters, representing uncertainty in the physics of interactions or in detector properties. Another complication, even with no nuisance parameters, is that the probability distributions of the models are specified only by simulation programs, with no way of evaluating their probability density functions. I advocate expressing the result of an experiment by means of the likelihood function, rather than by frequentist confidence intervals or p-values. A likelihood function for this problem is difficult to obtain, however, for both of the reasons given above. I discuss ways of circumventing these problems by reducing dimensionality using a classifier and employing simulations with multiple values for the nuisance parameters.