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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