The selection of variables in regression problems has occupied the minds of many statisticians. Several Bayesian variable selection methods have been developed, and we concentrate on the following methods: Kuo & Mallick, Gibbs Variable Selection (GVS), Stochastic Search Variable Selection (SSVS), adaptive shrinkage with Jeffreys' prior or a Laplacian prior, and reversible jump MCMC. We review these methods, in the context of their different properties. We then implement the methods in BUGS, using both real and simulated data as examples, and investigate how the different methods perform in practice. Our results suggest that SSVS, reversible jump MCMC and adaptive shrinkage methods can all work well, but the choice of which method is better will depend on the priors that are used, and also on how they are implemented.

R. B. O'Hara

M. J. Sillanpää

Bayesian Analysis

贝叶斯分析是国际贝叶斯分析学会的电子期刊。它旨在发表广泛的文章，在某些理论或应用背景下展示或讨论贝叶斯方法。该期刊欢迎提交新的计算和统计方法的投稿；对现有方法的批判性审查和讨论；历史观点；重要科学或政策应用领域的描述；实例探究;以及实验设计、数据收集、数据共享或数据挖掘的方法。提交的评估基于内容的重要性和沟通的有效性。讨论论文通常由主编选择，或由编辑建议，在定期提交的论文中。此外，《期刊》鼓励个人作者提交手稿以作为讨论文件考虑。

Bayesian Analysis is the electronic journal of the International Society for Bayesian Analysis. It aims to publish a wide range of articles that showcase or discuss Bayesian methods in various theoretical or applied contexts. The journal welcomes submissions of new computational and statistical methods; critical reviews and discussions of existing methods; historical perspectives; descriptions of significant scientific or policy application areas; case studies; as well as methods for experimental design, data collection, data sharing, or data mining. Submitted papers are evaluated based on the importance of their content and the effectiveness of their communication. Discussion papers are typically selected by the editor-in-chief or recommended by editors as part of regularly submitted papers. Additionally, Bayesian Analysis encourages individual authors to submit manuscripts for consideration as discussion papers.

《Bayesian Analysis》是国际贝叶斯分析学会的电子期刊，旨在发表广泛的文章，展示或讨论贝叶斯方法在各种理论或应用背景下的应用。该期刊欢迎提交新的计算和统计方法的研究；对现有方法的批判性审查和讨论；历史视角；重要科学或政策应用领域的描述；实例研究；以及实验设计、数据收集、数据共享或数据挖掘的方法。提交的论文将根据内容的重要性和沟通的有效性进行评估。讨论论文通常由主编选择，或由编辑建议，作为定期提交的论文的一部分。此外，《Bayesian Analysis》鼓励个人作者提交手稿，以供作为讨论文件考虑。

A review of Bayesian variable selection methods: what, how and which

The results suggest that SSVS, reversible jump MCMC and adaptive shrinkage methods can all work well, but the choice of which method is better will depend on the priors that are used, and also on how they are implemented.

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A review of Bayesian variable selection methods: what, how and which

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