# A binned likelihood for stochastic models

## TL;DR

This paper introduces a new analytic likelihood method that incorporates Monte Carlo uncertainties, improving model assessment accuracy in complex systems with limited or large datasets.

## Contribution

It presents a novel likelihood formulation that accounts for Monte Carlo uncertainties, enhancing statistical inference in complex stochastic models.

## Key findings

- Performs better than semi-analytic methods
- Prevents biased statistical claims
- Provides improved coverage properties

## Abstract

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.