A Pólya–Gamma sampler for a generalized logistic regression

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Abstract
In this paper, we introduce a novel Bayesian data augmentation approach for estimating the parameters of the generalized 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 algorithm performance is tested on simulated data. Furthermore, 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.
Funding Information
  • Chinese Fundamental Research Funds for the Central Universities (20720181062)
  • National Natural Science Foundation of China
  • European Community's Seventh Framework Programme (630677)
  • European Union Horizon 2020 Research and Innovation Programme (796902)

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