Silent coverage failures in rare-event searches and a degeneracy index that predicts them
Abstract
Searches for new physics in low-background experiments infer a non-negative signal strength from few events and often report an upper limit. Nominal frequentist coverage requires both a valid interval construction and an adequate data model. We study how controlled model departures affect lower- and upper-endpoint coverage for six interval procedures in an exact Poisson counting experiment, dark-matter recoil spectra, and a neutrinoless-double-beta-decay peak search. We introduce the Poisson--Fisher degeneracy index ℐPF(δν;ϑ0)=(β,γ), which maps a specified expected-count deformation, after projection onto the complete fitted tangent space, to β, the signed fitted signal shift in profiled standard-error units, and γ, the Poisson--Fisher norm of the unabsorbed residual. Locally, the sign of β identifies the threatened endpoint, while larger γ implies greater detectability by the saturated-Poisson goodness-of-fit test used here at a fixed 5% type-I error rate. Across the studied deformations, positive signal-like bias degrades discovery-side coverage while making upper limits conservative; negative signal bias from overestimated signal efficiency can make the upper endpoint undercover. Calibration under the nominal simulator does not protect against misspecification of that simulator relative to the data-generating process. A plausible deformation with large |β| and small γ may therefore evade diagnosis and should be represented by a nuisance constrained with auxiliary information or included in a defensible envelope. In the exactly collinear constrained-nuisance benchmark, modelling the deformation restores coverage at the evaluated grid points, at a quantifiable cost in interval sensitivity.
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BibTeX
@misc{pagano2026silent,
title = {{Silent coverage failures in rare-event searches and a degeneracy index that predicts them}},
author = {Davide Pagano},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2608.09203},
eprint = {2608.09203},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.09203},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Silent coverage failures in rare-event searches and a degeneracy index that predicts them
AU - Davide Pagano
PY - 2026
DA - 2026/10/09
PB - arXiv
DO - 10.48550/arxiv.2608.09203
UR - https://arxiv.org/abs/2608.09203
AB - Searches for new physics in low-background experiments infer a non-negative signal strength from few events and often report an upper limit. Nominal frequentist coverage requires both a valid interval construction and an adequate data model. We study how controlled model departures affect lower- and upper-endpoint coverage for six interval procedures in an exact Poisson counting experiment, dark-matter recoil spectra, and a neutrinoless-double-beta-decay peak search. We introduce the Poisson--Fisher degeneracy index ℐ_PF(δν;ϑ_0)=(β,γ), which maps a specified expected-count deformation, after projection onto the complete fitted tangent space, to β, the signed fitted signal shift in profiled standard-error units, and γ, the Poisson--Fisher norm of the unabsorbed residual. Locally, the sign of β identifies the threatened endpoint, while larger γ implies greater detectability by the saturated-Poisson goodness-of-fit test used here at a fixed 5% type-I error rate. Across the studied deformations, positive signal-like bias degrades discovery-side coverage while making upper limits conservative; negative signal bias from overestimated signal efficiency can make the upper endpoint undercover. Calibration under the nominal simulator does not protect against misspecification of that simulator relative to the data-generating process. A plausible deformation with large |β| and small γ may therefore evade diagnosis and should be represented by a nuisance constrained with auxiliary information or included in a defensible envelope. In the exactly collinear constrained-nuisance benchmark, modelling the deformation restores coverage at the evaluated grid points, at a quantifiable cost in interval sensitivity.
ER -