Posterior consistency in linear models under shrinkage priors
  We investigate the asymptotic behavior of posterior distributions of regression coefficients in high-dimensional linear models as the number of dimensions grows with the number of observations. We show that the posterior distribution concentrates in neighborhoods of the true parameter under simple sufficient conditions. These conditions hold under popular shrinkage priors given some sparsity assumptions. 
Artin Armagan, David B. Dunson, Jaeyong Lee, Waheed U. Bajwa, Nate   Strawn
stat.ME math.ST stat.TH