Mean-Tilted Intervals: Regression and Dynamic Models
Abstract
Mean-tilted intervals (MTIs) provide a fixed-content family of interval targets indexed by retained-mean balance. This paper develops generalized-Bayes computation for using those targets in regression and time-varying endpoint models after content and tilt have been specified. The update combines a prior with an exponentiated residual-product check loss, yielding uncertainty summaries for endpoint functions rather than a response-distribution model. A pseudo-asymmetric-Laplace normal-exponential representation gives generalized-inverse-Gaussian latent-scale updates and Gaussian conditional updates for one root when the other is fixed. The same representation gives deterministic ECM equations for generalized-posterior modes. We present ridge endpoint regression, a conditionally Gaussian shrinkage construction for the zero-tilt case, deterministic fixed-feature readouts, and dynamic linear endpoint states updated by alternating forward-filtering backward-sampling steps. These methods extend the MTI target from iid intervals to regression and dynamic settings; tolerance certification and response prediction require separate calibration or response models.
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BibTeX
@misc{leon2026meantilted,
title = {{Mean-Tilted Intervals: Regression and Dynamic Models}},
author = {Antonio De Leon and Raquel Prado and Bruno Sansó},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.13960},
eprint = {2610.13960},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.13960},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Mean-Tilted Intervals: Regression and Dynamic Models
AU - Antonio De Leon
AU - Raquel Prado
AU - Bruno Sansó
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.13960
UR - https://arxiv.org/abs/2610.13960
AB - Mean-tilted intervals (MTIs) provide a fixed-content family of interval targets indexed by retained-mean balance. This paper develops generalized-Bayes computation for using those targets in regression and time-varying endpoint models after content and tilt have been specified. The update combines a prior with an exponentiated residual-product check loss, yielding uncertainty summaries for endpoint functions rather than a response-distribution model. A pseudo-asymmetric-Laplace normal-exponential representation gives generalized-inverse-Gaussian latent-scale updates and Gaussian conditional updates for one root when the other is fixed. The same representation gives deterministic ECM equations for generalized-posterior modes. We present ridge endpoint regression, a conditionally Gaussian shrinkage construction for the zero-tilt case, deterministic fixed-feature readouts, and dynamic linear endpoint states updated by alternating forward-filtering backward-sampling steps. These methods extend the MTI target from iid intervals to regression and dynamic settings; tolerance certification and response prediction require separate calibration or response models.
ER -