Bring the noise: exact inference from noisy simulations in collider physics

TL;DR

This paper introduces an exact-approximate MCMC method for collider physics that provides precise inferences from noisy Monte Carlo simulations, demonstrating efficiency and robustness in LHC search analyses.

Contribution

It develops an unbiased estimator for Poisson likelihoods enabling exact inference from noisy simulations, a novel approach in collider data analysis.

Findings

Exact inferences achieved with similar computational cost to existing approximate methods.

Inferences are robust regardless of the number of simulated events per point.

The unbiased estimator is based on a Poisson-distributed number of MC events.

Abstract

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 pseudo-marginal 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.