Bayesian quantile additive regression trees

Quantile regression gives a comprehensive picture of the relationship between a response variable and a set of predictors. It is particularly appealing when the inferential interest lies in the probabilistic properties of extreme observations conditional on a set of predictors. Such objectives arise in various disciplines: in environmental sciences, Friederichs and Hense (2007) study the probabilistic properties of extreme precipitation events, while Pedersen (2015) model the tail distribution of stock and bond returns. In an epidemiological study, Burgette et al. (2011) use penalized quantile regression to explore covariates that affect the lower tail of the distribution of birth weight of babies. When the distribution of the dependent variable is skewed, the desire for robustness to extreme observations makes quantile regression a preferred approach. Examples include the study of tourist expense patterns in Marrocu et al. (2015) and wage distribution in Buchinsky (1995).