A simple sampler for the horseshoe estimator

TL;DR

This paper introduces a straightforward Bayesian sampling method for the horseshoe estimator in linear regression, offering new interpretations and extensions to logistic regression and alternative hierarchies, with efficient marginal likelihood computation.

Contribution

It presents a simple, conjugate Bayesian sampler for the horseshoe model, enhancing computational efficiency and interpretability, and discusses extensions to other models.

Findings

Efficient Bayesian sampler for horseshoe estimator

New interpretation of the horseshoe hierarchy

Extensions to logistic regression and horseshoe+

Abstract

In this note we derive a simple Bayesian sampler for linear regression with the horseshoe hierarchy. A new interpretation of the horseshoe model is presented, and extensions to logistic regression and alternative hierarchies, such as horseshoe$+$, are discussed. Due to the conjugacy of the proposed hierarchy, Chib's algorithm may be used to easily compute the marginal likelihood of the model.