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

Argüelles, C. A.; Schneider, A.; Yuan, T.

J. High Energy Phys. 2019, No. 6, Paper No. 30, 18 p. (2019).

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

Keywords:

event-by-event fluctuation; neutrino detectors and telescopes (experiments); unfolding

Software:

MCLLH; GitHub; HistFactory; emcee

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