Variable selection is a classic problem in statistics. In this paper, we consider a Bayes variable selection problem based on spike-and-slab prior with mixed normal distribution proposed by Ro\v{c}kov\'a and George (2014). Motivated by Ormerod and You(2017, 2022), we use the variational inference and collapsed variational inference method to solve the Bayesian problem instead of MCMC. Like Ormerod and You(2017, 2022), we also explain how the sparsity estimator is induced, and under certain mild assumptions, we also prove the consistent and asymptotic results.

翻译：变量选择是一个典型的统计问题。 在本文中, 我们考虑贝耶斯变量选择问题, 其依据是之前的钉杆和板块, 由 Ro\v{c}kov\\'a 和 George (2014年) 建议的混合正常分布。 由 Ormerod 和 You ( 2017, 2022年) 推动, 我们使用变式推论和崩溃的变式推论方法来解决巴伊西亚问题, 而不是 MCMC 。 像 Omerod 和 You ( 2017, 2022年) 一样, 我们还解释 如何引出 sparsity 估计器, 在某些温和的假设下, 我们还证明了 一致和无损的结果 。