{"ID":2856520,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.11708","arxiv_id":"2510.11708","title":"Simultaneous Frequentist Calibration of Confidence Regions for Multiple Functionals in Constrained Inverse Problems","abstract":"Many scientific analyses require simultaneous comparison of multiple functionals of an unknown signal at once, calling for multidimensional confidence regions with guaranteed simultaneous frequentist under structural constraints (e.g., non-negativity, shape, or physics-based). This paper unifies and extends many previous optimization-based approaches to constrained confidence region construction in linear inverse problems through the lens of statistical test inversion. We begin by reviewing the historical development of optimization-based confidence intervals for the single-functional setting, from \"strict bounds\" to the Burrus conjecture and its recent refutation via the aforementioned test inversion framework. We then extend this framework to the multiple-functional setting. This framework can be used to: (i) improve the calibration constants of previous methods, yielding smaller confidence regions that still preserve frequentist coverage, (ii) obtain tractable multidimensional confidence regions that need not be hyper-rectangles to better capture functional dependence structure, and (iii) generalize beyond Gaussian error distributions to generic log-concave error distributions. We provide theory establishing nominal simultaneous coverage of our methods and show quantitative volume improvements relative to prior approaches using numerical experiments.","short_abstract":"Many scientific analyses require simultaneous comparison of multiple functionals of an unknown signal at once, calling for multidimensional confidence regions with guaranteed simultaneous frequentist under structural constraints (e.g., non-negativity, shape, or physics-based). This paper unifies and extends many previo...","url_abs":"https://arxiv.org/abs/2510.11708","url_pdf":"https://arxiv.org/pdf/2510.11708v1","authors":"[\"Pau Batlle\",\"Pratik Patil\",\"Michael Stanley\",\"Javier Ruiz Lupon\",\"Houman Owhadi\",\"Mikael Kuusela\"]","published":"2025-10-13T17:58:56Z","proceeding":"math.ST","tasks":"[\"math.ST\"]","methods":"[]","has_code":false}