A binned likelihood for stochastic models

Metrics of model goodness-of-fit, model comparison, and model parameter estimation are the main categories of statistical problems in science. Bayesian and frequentist methods that address these questions often rely on a likelihood function, which describes the plausibility of model parameters given observed data. In some complex systems or experimental setups predicting the outcome of a model cannot be done analytically and Monte Carlo techniques are used. In this paper, we present a new analytic likelihood that takes into account Monte Carlo uncertainties, appropriate for use in large or small statistics regimes. Our formulation has better performance than semi-analytic methods, prevents strong claims on biased statements, and results in better coverage properties than available methods.