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Statistical techniques used in air pollution modelling usually lack thepossibility to understand which predictors affect air pollution in whichfunctional form; and are not able to regress on exceedances over certainthresholds imposed by authorities directly. The latter naturally induceconditional quantiles and reflect the seriousness of particular events. In thepresent paper we focus on this important aspect by developing quantileregression models further. We propose a general Bayesian effect selectionapproach for additive quantile regression within a highly interpretableframework. We place separate normal beta prime spike and slab priors on thescalar importance parameters of effect parts and implement a fast Gibbssampling scheme. Specifically, it enables to study quantile-specific covariateeffects, allows these covariates to be of general functional form usingadditive predictors, and facilitates the analysts' decision whether an effectshould be included linearly, non-linearly or not at all in the quantiles ofinterest. In a detailed analysis on air pollution data in Madrid (Spain) wefind the added value of modelling extreme nitrogen dioxide (NO2) concentrationsand how thresholds are driven differently by several climatological variablesand traffic as a spatial proxy. Our results underpin the need of enhancedstatistical models to support short-term decisions and enable local authoritiesto mitigate or even prevent exceedances of NO2 concentration limits.

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