We consider Bayesian logistic regression models with group-structured covariates. In high-dimensional settings, it is often assumed that only a small portion of groups are significant, thus consistent group selection is of significant importance. While consistent frequentist group selection methods have been proposed, theoretical properties of Bayesian group selection methods for logistic regression models have not been investigated yet. In this paper, we consider a hierarchical group spike and slab prior for logistic regression models in high-dimensional settings. Under mild conditions, we establish strong group selection consistency of the induced posterior, which is the first theoretical result in the Bayesian literature. Through simulation studies, we demonstrate that the proposed method outperforms existing state-of-the-art methods in various settings. We further apply our method to an MRI data set for predicting Parkinson's disease and show its benefits over other contenders. This article is protected by copyright. All rights reserved.

中文翻译：

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贝叶斯组选择在逻辑回归中应用于 MRI 数据分析

我们考虑具有组结构协变量的贝叶斯逻辑回归模型。在高维设置中，通常假设只有一小部分组是重要的，因此一致的组选择非常重要。虽然已经提出了一致的频率论组选择方法，但尚未研究用于逻辑回归模型的贝叶斯组选择方法的理论特性。在本文中，我们考虑了高维设置中逻辑回归模型的分层组尖峰和平板先验。在温和条件下，我们建立了诱导后验的强组选择一致性，这是贝叶斯文献中的第一个理论结果。通过模拟研究，我们证明了所提出的方法在各种设置中都优于现有的最先进方法。我们进一步将我们的方法应用于 MRI 数据集以预测帕金森病，并展示其优于其他竞争者的优势。本文受版权保护。版权所有。