PreprintCC BY-NC-ND 4.0arXiv
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.
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BibTeX
@misc{kulkarni2026pathwise,
title = {{Pathwise Shrinkage and Probabilistic Calibration of the Multiplicative Half-Cauchy Process}},
author = {Siddhesh Kulkarni},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.21136},
eprint = {2610.21136},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.21136},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Pathwise Shrinkage and Probabilistic Calibration of the Multiplicative Half-Cauchy Process
AU - Siddhesh Kulkarni
PY - 2026
DA - 2026/10/15
PB - arXiv
DO - 10.48550/arxiv.2610.21136
UR - https://arxiv.org/abs/2610.21136
AB - 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.
ER -