The Grouped Horseshoe distribution and its statistical properties

TL;DR

This paper introduces the Grouped Horseshoe distribution, analyzing its properties and implications for Bayesian inference, especially in the context of selecting groups of regression coefficients.

Contribution

It isolates and studies the properties of the Grouped Horseshoe distribution, extending understanding of its behavior in Bayesian hierarchical models.

Findings

Most properties of the univariate Horseshoe transfer to the grouped case

The distribution is useful for group selection in Bayesian regression

Some properties do not transfer, indicating unique features

Abstract

The Grouped Horseshoe distribution arises from hierarchical structures in the recent Bayesian methodological literature aimed at selection of groups of regression coefficients. We isolate this distribution and study its properties concerning Bayesian statistical inference. Most, but not all, of the properties of the univariate Horseshoe distribution are seen to transfer to the grouped case.