## A binned likelihood for stochastic models.(English)Zbl 1416.62698

Summary: 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.

### MSC:

 62P35 Applications of statistics to physics 85A35 Statistical astronomy 65C05 Monte Carlo methods

### Software:

GitHub; MCLLH; emcee; HistFactory
Full Text:

### References:

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