Pathwise Shrinkage and Probabilistic Calibration of the Multiplicative Half-Cauchy Process

Abstract:We characterize the multiplicative half-Cauchy process through its log-scale random-walk representation, establishing shrinkage, expansion, and critical regimes, almost-sure summability, local rebounds, and effective dimension. We also derive a semi-analytic calibration rule linking interpretable prior probability statements to its scale parameter.

6 pages, 1 figure, 1 table. R package: this https URL. Software DOI: https://doi.org/10.5281/zenodo.23355811

Methodology (stat.ME); Machine Learning (cs.LG); Probability (math.PR); Statistics Theory (math.ST)

arXiv:2610.21136 [stat.ME]

(or arXiv:2610.21136v1 [stat.ME] for this version)

https://doi.org/10.48550/arXiv.2610.21136 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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