Distributional regression forests for probabilistic precipitation forecasting in complex terrain

Lisa Schlosser (), Torsten Hothorn (), Reto Stauffer () and Achim Zeileis ()

Working Papers from Faculty of Economics and Statistics, Universität Innsbruck

Abstract: 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 non-homogenous Gaussian regression (NGR) models both mean and variance of a Gaussian response and is particularly popular in weather forecasting. More generally, the GAMLSS framework allows to establish generalized additive models for location, scale, and shape with smooth linear or nonlinear effects. However, when variable selection is required and/or there are non-smooth 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.

Keywords: parametric models; regression trees; random forests; recursive partitioning; probabilistic forecasting; GAMLSS (search for similar items in EconPapers)
Pages: 76 pages
Date: 2018-08, Revised 2018-11
New Economics Papers: this item is included in nep-cmp, nep-ecm and nep-for
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Persistent link: https://EconPapers.repec.org/RePEc:inn:wpaper:2018-08

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