A Pólya-Gamma Sampler for a Generalized Logistic Regression

In this paper we introduce a novel Bayesian data augmentation approach for estimating the parameters of the generalised logistic regression model. We propose a Pólya-Gamma sampler algorithm that allows us to sample from the exact posterior distribution, rather than relying on approximations. A simul...

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Bibliographic Details
Published in:arXiv.org 2020-12
Main Authors: Luciana Dalla Valle, Leisen, Fabrizio, Rossini, Luca, Zhu, Weixuan
Format: Article
Language:English
Subjects:
Algorithms
Computer simulation
Parameter estimation
Regression models
Online Access:Get full text
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Summary:In this paper we introduce a novel Bayesian data augmentation approach for estimating the parameters of the generalised logistic regression model. We propose a Pólya-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 Pólya-Gamma sampler provides more precise estimates than the empirical likelihood method, outperforming approximate approaches.
ISSN:2331-8422