A1414
Title: Bayesian variable selection for structured quantile regression
Authors: Giovanni Luzzatto - University of Padova (Italy) [presenting]
Mauro Bernardi - University of Padova (Italy)
Marina Bertolini - University of Padova (Italy)
Rubina Canesi - University of Padova (Italy)
Luca Doretti - University of Padova (Italy)
Duccio Gamannossi Degl\'Innocenti - University of Padova (Italy)
Abstract: Quantile regression provides a flexible framework for modeling heterogeneous covariate effects across the conditional distribution of a response variable. In many applications, relevant predictors exhibit nonlinear, spatial, temporal, or spatio-temporal effects, requiring structured semiparametric specifications. While latent Gaussian models provide a flexible framework for incorporating such dependencies through spline-based and SPDE representations, scalable variable selection procedures for structured effects remain underdeveloped. A Bayesian model selection framework for spatio-temporal quantile regression is presented, combining spike-and-slab priors with latent Gaussian models to simultaneously perform selection of linear covariates, nonlinear functional components, and structured spatial and temporal effects. Structured shrinkage priors are introduced to identify relevant predictors while preserving local smoothness and dependence properties. Posterior inference is based on a latent-variable representation of the asymmetric Laplace likelihood coupled with efficient MCMC algorithms. The methodology provides automatic complexity control, uncertainty quantification, and interpretable posterior inclusion probabilities for both fixed and structured effects. Simulation studies and empirical applications demonstrate the ability of the approach to recover heterogeneous effects across quantiles while identifying key structured components driving the response distribution.
