  In this paper, we consider Bayesian variable selection problem of linear
regression model with global-local shrinkage priors on the regression
coefficients. We propose a variable selection procedure that select a variable
if the ratio of the posterior mean to the ordinary least square estimate of the
corresponding coefficient is greater than $1/2$. Under the assumption of
orthogonal designs, we show that if the local parameters have polynomial-tailed
priors, our proposed method enjoys the oracle property in the sense that it can
achieve variable selection consistency and optimal estimation rate at the same
time. However, if, instead, an exponential-tailed prior is used for the local
parameters, the proposed method does not have the oracle property.
