  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, 2023), we use the variational inference and
collapsed variational inference method to solve the Bayesian problem instead of
MCMC. Like Ormerod and You (2017, 2023), we also explain how the sparsity
estimator is induced, and under certain mild assumptions, we also prove the
consistent and asymptotic results.
