Pathwise Shrinkage and Probabilistic Calibration of the Multiplicative Half-Cauchy Process
stat.ME, cs.LG, math.PR, math.ST, stat.TH
Submitted: 2026-10-15
Updated: 2026-10-15
Comments: 6 pages, 1 figure, 1 table. R package: https://github.com/SiddheshKulkarni-source/mhcp. Software DOI: 10.5281/zenodo.23355811
License: http://creativecommons.org/licenses/by-nc-nd/4.0/
The gist: We characterize the multiplicative half-Cauchy process through its log-scale random-walk representation, establishing shrinkage, expansion, and critical regimes, almost-sure summability, local
Terminology
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.
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