  A nonparametric Bayes approach is proposed for the problem of estimating a
sparse sequence based on Gaussian random variables. We adopt the popular
two-group prior with one component being a point mass at zero, and the other
component being a mixture of Gaussian distributions. Although the Gaussian
family has been shown to be suboptimal for this problem, we find that Gaussian
mixtures, with a proper choice on the means and mixing weights, have the
desired asymptotic behavior, e.g., the corresponding posterior concentrates on
balls with the desired minimax rate. To achieve computation efficiency, we
propose to obtain the posterior distribution using a deterministic variational
algorithm. Empirical studies on several benchmark data sets demonstrate the
superior performance of the proposed algorithm compared to other alternatives.
