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Unfolding is an ill-posed inverse problem in particle physics aiming to infera true particle-level spectrum from smeared detector-level data. Forcomputational and practical reasons, these spaces are typically discretizedusing histograms, and the smearing is modeled through a response matrixcorresponding to a discretized smearing kernel of the particle detector. Thisresponse matrix depends on the unknown shape of the true spectrum, leading to afundamental systematic uncertainty in the unfolding problem. To handle theill-posed nature of the problem, common approaches regularize the problemeither directly via methods such as Tikhonov regularization, or implicitly byusing wide-bins in the true space that match the resolution of the detector.Unfortunately, both of these methods lead to a non-trivial bias in the unfoldedestimator, thereby hampering frequentist coverage guarantees for confidenceintervals constructed from these methods. We propose two new approaches toaddressing the bias in the wide-bin setting through methods calledOne-at-a-time Strict Bounds (OSB) and Prior-Optimized (PO) intervals. The OSBintervals are a bin-wise modification of an existing guaranteed-coverageprocedure, while the PO intervals are based on a decision-theoretic view of theproblem. Importantly, both approaches provide well-calibrated frequentistconfidence intervals even in constrained and rank-deficient settings. Thesemethods are built upon a more general answer to the wide-bin bias problem,involving unfolding with fine bins first, followed by constructing confidenceintervals for linear functionals of the fine-bin counts. We test and comparethese methods to other available methodologies in a wide-bin deconvolutionexample and a realistic particle physics simulation of unfolding a steeplyfalling particle spectrum.

Uncertainty quantification for wide-bin unfolding: one-at-a-time strict bounds and prior-optimized confidence intervals