Exact inference from noisy simulations in collider physics

We rely on Monte Carlo (MC) simulations to interpret searches for new physics at the Large Hadron Collider (LHC) and elsewhere. These simulations result in noisy and approximate estimators of selection efficiencies and likelihoods. In this context we pioneer an exact-approximate computational method—exact-approximate Markov chain Monte Carlo (MCMC), also known as pseudomarginal MCMC—that returns exact inferences despite noisy simulations. To do so, we introduce an unbiased estimator for a Poisson likelihood. We demonstrate the new estimator and new techniques in examples based on a search for neutralinos and charginos at the LHC using a simplified model. We find attractive performance characteristics—exact inferences are obtained for a similar computational cost to approximate ones from existing methods and inferences are robust with respect to the number of events generated per point. The unbiased estimator uses a Poisson-distributed number of MC events; it is also possible to construct a biased estimator whose bias decays factorially with increasing number of MC events.