Open Access
September 2019 Distributional regression forests for probabilistic precipitation forecasting in complex terrain
Lisa Schlosser, Torsten Hothorn, Reto Stauffer, Achim Zeileis
Ann. Appl. Stat. 13(3): 1564-1589 (September 2019). DOI: 10.1214/19-AOAS1247


To obtain a probabilistic model for a dependent variable based on some set of explanatory variables, a distributional approach is often adopted where the parameters of the distribution are linked to regressors. In many classical models this only captures the location of the distribution but over the last decade there has been increasing interest in distributional regression approaches modeling all parameters including location, scale and shape. Notably, so-called nonhomogeneous Gaussian regression (NGR) models both mean and variance of a Gaussian response and is particularly popular in weather forecasting. Moreover, generalized additive models for location, scale and shape (GAMLSS) provide a framework where each distribution parameter is modeled separately capturing smooth linear or nonlinear effects. However, when variable selection is required and/or there are nonsmooth dependencies or interactions (especially unknown or of high-order), it is challenging to establish a good GAMLSS. A natural alternative in these situations would be the application of regression trees or random forests but, so far, no general distributional framework is available for these. Therefore, a framework for distributional regression trees and forests is proposed that blends regression trees and random forests with classical distributions from the GAMLSS framework as well as their censored or truncated counterparts. To illustrate these novel approaches in practice, they are employed to obtain probabilistic precipitation forecasts at numerous sites in a mountainous region (Tyrol, Austria) based on a large number of numerical weather prediction quantities. It is shown that the novel distributional regression forests automatically select variables and interactions, performing on par or often even better than GAMLSS specified either through prior meteorological knowledge or a computationally more demanding boosting approach.


Download Citation

Lisa Schlosser. Torsten Hothorn. Reto Stauffer. Achim Zeileis. "Distributional regression forests for probabilistic precipitation forecasting in complex terrain." Ann. Appl. Stat. 13 (3) 1564 - 1589, September 2019.


Received: 1 November 2018; Revised: 1 February 2019; Published: September 2019
First available in Project Euclid: 17 October 2019

zbMATH: 07145968
MathSciNet: MR4019150
Digital Object Identifier: 10.1214/19-AOAS1247

Keywords: GAMLSS , Parametric models , probabilistic forecasting , random forests , recursive partitioning , regression trees

Rights: Copyright © 2019 Institute of Mathematical Statistics

Vol.13 • No. 3 • September 2019
Back to Top