  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 is the key ingredient in order to assess 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 the large and small sample size limits. Our formulation performs better
than semi-analytic methods, prevents strong claims on biased statements, and
provides improved coverage properties compared to available methods.
