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Title: A Dirichlet process mixture model for nonparametric Bayesian quantile regression Authors:  Nan Lin - Washington University in St. Louis (United States) [presenting]
Abstract: A new nonparametric Bayesian approach to quantile regression is proposed by using a Dirichlet process mixture of logistic distributions (DPML). Many existing Bayesian quantile regression methods are based on parametric substitution of the error distribution by the asymmetric Laplace distribution, which is inconsistent with the typical nonparametric nature of quantile regression. The logistic distribution has a simple form in its quantile function and hence easily accommodates the quantile constraint. The proposed DPML model enjoys great model flexibility by mixing over both the location parameter and the scale parameter. We further established the posterior consistency of our proposed model and provided Markov chain Monte Carlo algorithms for posterior inference. The performance of our approaches is evaluated using simulated data and real data.