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.

在本文中，我们介绍了一种新的贝叶斯数据增强方法，用于估计广义逻辑回归模型的参数。我们提出了一种 Pólya-Gamma 采样器算法，它允许我们从精确的后验分布中进行采样，而不是依赖于近似值。模拟研究说明了所提出的方法在不同维度的二元响应数据中捕获重尾和轻尾的灵活性和准确性。算法性能在模拟数据上进行测试。此外，该方法应用于两个不同的真实数据集，我们证明了 Pólya-Gamma 采样器提供比经验似然方法更精确的估计，优于近似方法。