Analysis of MCMC algorithms for Bayesian linear regression with Laplace errors
Journal of Multivariate Analysis
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Consider the quantile regression model Y=X@b+@s@e where the components of @e are i.i.d. errors from the asymmetric Laplace distribution with rth quantile equal to 0, where r@?(0,1) is fixed. Kozumi and Kobayashi (2011) [9] introduced a Gibbs sampler that can be used to explore the intractable posterior density that results when the quantile regression likelihood is combined with the usual normal/inverse gamma prior for (@b,@s). In this paper, the Markov chain underlying Kozumi and Kobayashi's (2011) [9] algorithm is shown to converge at a geometric rate. No assumptions are made about the dimension of X, so the result still holds in the ''large p, small n'' case.