  Two-component mixture priors provide a traditional way to induce sparsity in
high-dimensional Bayes models. However, several aspects of such a prior,
including computational complexities in high-dimensions, interpretation of
exact zeros and non-sparse posterior summaries under standard loss functions,
has motivated an amazing variety of continuous shrinkage priors, which can be
expressed as global-local scale mixtures of Gaussians. Interestingly, we
demonstrate that many commonly used shrinkage priors, including the Bayesian
Lasso, do not have adequate posterior concentration in high-dimensional
settings.
