Bayesian variable selection and estimation in quantile regression using a quantile-specific prior
Mai Dao, Min Wang, Souparno Ghosh, Keying Ye
Keywords: Quantile regression, variable selection
Asymmetric Laplace (AL) specification has become one of ideal statistical models for Bayesian quantile regression
analysis. Besides fast convergence of Markov Chain Monte Carlo (MCMC), AL specification guarantees posterior
consistency even under model misspecification. However, variable selection under such a specification is a daunting
task because, realistically, prior specification of regression parameters should take the quantile levels into consideration.
Quantile-specific Zellner’s $g$-prior has recently been proposed for Bayesian variable selection in quantile regression,
whereas it comes at a high price of the computational burden due to the intractability of the posterior distributions.
This poster shows that a fast computation can be achieved with exact, but intractable posterior distributions. We
devise a three-stage computational scheme starting with an expectation-maximization (EM) algorithm and then the
Gibbs sampler followed by an importance re-weighting step. The performance and effectiveness of the proposed
procedure are illustrated with both simulation studies and a real-data application. Numerical results suggest that the
proposed procedure compares favorably with the exact MCMC algorithm.