A comparison study of Bayesian high-dimensional linear regression models

초록

We consider linear regression models in high-dimensional settings (p >> n) and compare various classes of priors. The spike and slab prior is one of the most widely used priors for Bayesian regression models, but its model space is vast, resulting in a bad performance in finite samples. As an alternative, various continuous shrinkage priors, including the horseshoe prior and its variants, have been proposed. Although each of the above priors has been investigated separately, exhaustive comparative studies of their performance have been conducted very rarely. In this study, we compare the spike and slab prior, the horseshoe prior and its variants in various simulation settings. The performance of each method is demonstrated in terms of the regression coefficient estimation and variable selection. Finally, some remarks and suggestions are given based on comprehensive simulation studies.

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