A P\'olya-Gamma Sampler for a Generalized Logistic Regression

TL;DR

This paper introduces a Pólya-Gamma data augmentation method for Bayesian generalized logistic regression, enabling exact posterior sampling and improving estimation accuracy over approximate methods.

Contribution

It presents a novel Pólya-Gamma sampler for Bayesian generalized logistic regression, allowing exact posterior inference and better tail modeling.

Findings

Sampler accurately captures heavy and light tails.

Outperforms empirical likelihood in real data applications.

Provides more precise estimates than approximate methods.

Abstract

In this paper we introduce a novel Bayesian data augmentation approach for estimating the parameters of the generalised logistic regression model. We propose a P\'olya-Gamma sampler algorithm that allows us to sample from the exact posterior distribution, rather than relying on approximations. A simulation study illustrates the flexibility and accuracy of the proposed approach to capture heavy and light tails in binary response data of different dimensions. The methodology is applied to two different real datasets, where we demonstrate that the P\'olya-Gamma sampler provides more precise estimates than the empirical likelihood method, outperforming approximate approaches.