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.

arXiv comment6 pages, 1 figure, 1 table. R package: https://github.com/SiddheshKulkarni-source/mhcp. Software DOI: 10.5281/zenodo.23355811