MCMC for Global-Local Shrinkage Priors in High-Dimensional Settings
Anirban Bhattacharya, James E. Johndrow · 2021
In this chapter, we provide a review of MCMC computation with one-group or continuous shrinkage priors expressed as scale mixtures of Gaussians in the high-dimensional regression model. We primarily focus on blocked Gibbs samplers, which are popularly used in hierarchical Gaussian models. For sake of concreteness, we additionally focus on the popular horseshoe prior while pointing out generalizations whenever appropriate. Our discussions span various blocking strategies, computational complexities, numerical issues, and geometric convergence. We conclude with some topics for future research.