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Distributional regression forests for probabilistic precipitation forecasting in complex terrain

Author

Listed:
  • Lisa Schlosser
  • Torsten Hothorn
  • Reto Stauffer
  • Achim Zeileis
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.

Suggested Citation

  • Lisa Schlosser & Torsten Hothorn & Reto Stauffer & Achim Zeileis, 2018. "Distributional regression forests for probabilistic precipitation forecasting in complex terrain," Working Papers 2018-08, Faculty of Economics and Statistics, Universität Innsbruck, revised Nov 2018.
    • Handle: RePEc:inn:wpaper:2018-08
    as

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    File URL: https://www2.uibk.ac.at/downloads/c4041030/wpaper/2018-08.pdf
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    References listed on IDEAS

    as
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    2. Hofner, Benjamin & Mayr, Andreas & Schmid, Matthias, 2016. "gamboostLSS: An R Package for Model Building and Variable Selection in the GAMLSS Framework," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 74(i01).
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    5. R. A. Rigby & D. M. Stasinopoulos, 2005. "Generalized additive models for location, scale and shape," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 54(3), pages 507-554, June.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    parametric models; regression trees; random forests; recursive partitioning; probabilistic forecasting; GAMLSS;
    All these keywords.

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