Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Uncertainty quantification for wide-bin unfolding: one-at-a-time strict
  bounds and prior-optimized confidence intervals   Unfolding is an ill-posed inverse problem in particle physics aiming to infer
a true particle-level spectrum from smeared detector-level data. For
computational and practical reasons, these spaces are typically discretized
using histograms, and the smearing is modeled through a response matrix
corresponding to a discretized smearing kernel of the particle detector. This
response matrix depends on the unknown shape of the true spectrum, leading to a
fundamental systematic uncertainty in the unfolding problem. To handle the
ill-posed nature of the problem, common approaches regularize the problem
either directly via methods such as Tikhonov regularization, or implicitly by
using 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 unfolded
estimator, thereby hampering frequentist coverage guarantees for confidence
intervals constructed from these methods. We propose two new approaches to
addressing the bias in the wide-bin setting through methods called
One-at-a-time Strict Bounds (OSB) and Prior-Optimized (PO) intervals. The OSB
intervals are a bin-wise modification of an existing guaranteed-coverage
procedure, while the PO intervals are based on a decision-theoretic view of the
problem. Importantly, both approaches provide well-calibrated frequentist
confidence intervals even in constrained and rank-deficient settings. These
methods are built upon a more general answer to the wide-bin bias problem,
involving unfolding with fine bins first, followed by constructing confidence
intervals for linear functionals of the fine-bin counts. We test and compare
these methods to other available methodologies in a wide-bin deconvolution
example and a realistic particle physics simulation of unfolding a steeply
falling particle spectrum.

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The categories of this paper are: solv-int
14
The categories of this paper are: math-ph
18
The categories of this paper are: econ
4
The categories of this paper are: cond-mat
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The categories of this paper are: nlin
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The categories of this paper are: adap-org
5
The categories of this paper are: gr-qc
6
The categories of this paper are: astro-ph
2
The categories of this paper are: math
27
The categories of this paper are: comp-gas
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The categories of this paper are: plasm-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: quant-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-th
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The categories of this paper are: alg-geom