L1-norm regularized logistic regression models are widely used for analyzing data with binary response. In those analyses, fusing regression coefficients is useful for detecting groups of variables. This paper proposes a binomial logistic regression model with Bayesian fused lasso. Assuming a Laplace prior on regression coefficients and differences between adjacent regression coefficients enables us to perform variable selection and variable fusion simultaneously in the Bayesian framework. We also propose assuming a horseshoe prior on the differences to improve the flexibility of variable fusion. The Gibbs sampler is derived to estimate the parameters by a hierarchical expression of priors and a data-augmentation method. Using simulation studies and real data analysis, we compare the proposed methods with the existing method.

翻译：L1范数正则化逻辑回归模型广泛应用于分析二元响应数据。在此类分析中，融合回归系数有助于检测变量组。本文提出了一种带有贝叶斯融合Lasso的二项逻辑回归模型。通过假设回归系数及其相邻差分的拉普拉斯先验，我们能够在贝叶斯框架中同时实现变量选择和变量融合。我们还假设差分的马蹄形先验以增强变量融合的灵活性。利用先验的层次化表示和数据增广方法，推导了吉布斯采样器用于参数估计。通过模拟研究和真实数据分析，我们将所提方法与现有方法进行了比较。