A key issue when using Bayesian variable selection for logistic regression is choosing an appropriate prior distribution. This can be particularly difficult for high‐dimensional data where complete separation will naturally occur in the high‐dimensional space. We propose the use of the Normal‐Gamma prior with recommendations on calibration of the hyper‐parameters. We couple this choice with the use of joint credible sets to avoid performing a search over the high‐dimensional model space. The approach is shown to outperform other methods in high‐dimensional settings, especially with highly correlated data. The Bayesian approach allows for a natural specification of the hyper‐parameters.

中文翻译：

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贝叶斯变量选择用于逻辑回归

使用贝叶斯变量选择进行逻辑回归时的关键问题是选择合适的先验分布。对于在高维空间中自然发生完全分离的高维数据，这可能尤其困难。我们建议先使用正态伽玛，再建议对超参数进行校准。我们将此选择与联合可信集结合使用，以避免在高维模型空间上执行搜索。在高维环境中，该方法表现出优于其他方法，尤其是在高度相关的数据中。贝叶斯方法允许对超参数进行自然规范。