A binned likelihood for stochastic models

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.

18 pages, 7 figures, 2 tables, code can be found at https://github.com/austinschneider/MCLLH

References in corpus (6)

• emcee: The MCMC Hammer
• A binned likelihood for stochastic models
• Statistics of weighted Poisson events and its applications
• Exploring Theory Space with Monte Carlo Reweighting
• Probabilistic treatment of the uncertainty from the finite size of weighted Monte Carlo data
• Neutrino oscillations: ILL experiment revisited

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