  We consider a sparse linear regression model with unknown symmetric error
under the high-dimensional setting. The true error distribution is assumed to
belong to the locally $\beta$-H\"{o}lder class with an exponentially decreasing
tail, which does not need to be sub-Gaussian. We obtain posterior convergence
rates of the regression coefficient and the error density, which are nearly
optimal and adaptive to the unknown sparsity level. Furthermore, we derive the
semi-parametric Bernstein-von Mises (BvM) theorem to characterize asymptotic
shape of the marginal posterior for regression coefficients. Under the
sub-Gaussianity assumption on the true score function, strong model selection
consistency for regression coefficients are also obtained, which eventually
asserts the frequentist's validity of credible sets.
