A model independent safeguard for unbinned Likelihood

Abstract

We present a universal method to include residual un-modeled background shape uncertainties in likelihood based statistical tests for high energy physics and astroparticle physics. This approach provides a simple and natural protection against mismodeling, thus lowering the chances of a false discovery or of an over constrained confidence interval, and allows a natural transition to unbinned space. Unbinned likelihood allows optimal usage of information for the data and the models, and enhances the sensitivity. We show that the asymptotic behavior of the test statistic can be regained in cases where the model fails to describe the true background behavior, and present 1D and 2D case studies for model-driven and data-driven background models. The resulting penalty on sensitivities follows the actual discrepancy between the data and the models, and is asymptotically reduced to zero with increasing knowledge.

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• Constraining the Spin-Dependent WIMP-Nucleon Cross Sections with XENON1T
• XENON1T Dark Matter Data Analysis: Signal & Background Models, and Statistical Inference
• Searching for new physics with profile likelihoods: Wilks and beyond
• New constraints and discovery potential of sub-GeV dark matter with xenon detectors
• Investigating the XENON1T Low-Energy Electronic Recoil Excess Using NEST
• Detecting new signals under background mismodelling
• Effective field theory and inelastic dark matter results from XENON1T
• XENONnT WIMP Search: Signal & Background Modeling and Statistical Inference
• Informative Goodness-of-Fit for Multivariate Distributions
• Deficit hawks: robust new physics searches with unknown backgrounds