• The Korean Journal of Applied Statistics
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• v.35 no.2
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• pp.285-298
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• 2022

Continuous shrinkage priors, as well as spike and slab priors, have been widely employed for Bayesian inference about sparse regression coefficient vectors or covariance matrices. Continuous shrinkage priors provide computational advantages over spike and slab priors since their model space is substantially smaller. This is especially true in high-dimensional settings. However, variable selection based on continuous shrinkage priors is not straightforward because they do not give exactly zero values. Although few variable selection approaches based on continuous shrinkage priors have been proposed, no substantial comparative investigations of their performance have been conducted. In this paper, We compare two variable selection methods: a credible interval method and the sequential 2-means algorithm (Li and Pati, 2017). Various simulation scenarios are used to demonstrate the practical performances of the methods. We conclude the paper by presenting some observations and conjectures based on the simulation findings.

• The Korean Journal of Applied Statistics
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• v.34 no.3
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• pp.491-505
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• 2021

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.