Bayesian inference for structured additive quantile regression models

Most quantile regression problems in practice require flexible semiparametric forms of the predictor for modeling the dependence of responses on covariates. Furthermore, it is often necessary to add random effects accounting for overdispersion caused by unobserved heterogeneity or for correlation in longitudinal data. We present a unified approach for Bayesian quantile inference via Markov chain Monte Carlo (MCMC) simulation and approximate inference using integrated nested Laplace approximations (INLA) in additive and semiparametric mixed models. Different types of covariates are all treated within the same general framework by assigning appropriate Gaussian Markov random field (GMRF) priors with different forms and degrees of smoothness. We applied the approach in several simulation and case studies, showing that the methods are also computationally efficient in problems with many covariates and large datasets.