ABSTRACT
In ecology specifically, B. Cade and B. Noon advocated the use of quantile regression methods for ecological inference, but the details on how to implement and extend quantile regression models. This chapter provides a short introduction to the concept of quantile regression and shows how to extend this concept to the Bayesian setting. It presents different and contrasting perspectives on quantile regression and describes how use it in ecological and environmental science. Quantile regression arose as an alternative to testing for homoskedasticity and conditional symmetry in regression models. Quantile regression has been extended also to the spatial and spatio-temporal setting. There are many alternatives to quantile regression that relax the assumptions associated with conventional mean regression. The chapter also presents Bayesian expectile regression results in the use of an asymmetric normal distribution for a data model instead of the asymmetric Laplace distribution.
