Bayesian Effect Selection for Additive Quantile Regression with an Analysis to Air Pollution Thresholds

TL;DR

This paper introduces a Bayesian effect selection method for additive quantile regression, allowing detailed analysis of predictors' effects on air pollution thresholds, especially for extreme nitrogen dioxide levels in Madrid.

Contribution

It develops a novel Bayesian approach with spike and slab priors for effect selection in additive quantile regression, enabling flexible modeling of covariate effects and threshold exceedances.

Findings

Identified key climatological and traffic variables influencing NO2 thresholds.

Demonstrated the method's ability to distinguish linear and nonlinear effects.

Provided insights for policy decisions to prevent air quality exceedances.

Abstract

Statistical techniques used in air pollution modelling usually lack the possibility to understand which predictors affect air pollution in which functional form; and are not able to regress on exceedances over certain thresholds imposed by authorities directly. The latter naturally induce conditional quantiles and reflect the seriousness of particular events. In the present paper we focus on this important aspect by developing quantile regression models further. We propose a general Bayesian effect selection approach for additive quantile regression within a highly interpretable framework. We place separate normal beta prime spike and slab priors on the scalar importance parameters of effect parts and implement a fast Gibbs sampling scheme. Specifically, it enables to study quantile-specific covariate effects, allows these covariates to be of general functional form using additive predictors, and facilitates the analysts' decision whether an effect should be included linearly, non-linearly or not at all in the quantiles of interest. In a detailed analysis on air pollution data in Madrid (Spain) we find the added value of modelling extreme nitrogen dioxide (NO2) concentrations and how thresholds are driven differently by several climatological variables and traffic as a spatial proxy. Our results underpin the need of enhanced statistical models to support short-term decisions and enable local authorities to mitigate or even prevent exceedances of NO2 concentration limits.