Cholesky-based multivariate gaussian regression

• Thomas Muschinski ^[1] ; Georg von Mayr ; Thorsten Simon ; Achim Zeileis
  1. [1] University of Innsbruck

     University of Innsbruck

     Innsbruck, Austria

     
• Localización: Proceedings of the 35th International Workshop on Statistical Modelling : July 20-24, 2020 Bilbao, Basque Country, Spain / Itziar Irigoien Garbizu (ed. lit.), Dae-Jin Lee (ed. lit.), Joaquín Martínez Minaya (ed. lit.), María Xosé Rodríguez Álvarez (ed. lit.), 2020, ISBN 978-84-1319-267-3, págs. 382-385
• Idioma: inglés
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• Resumen

  • Multivariate Gaussian regression has applications in many elds, but is made dicult by the high model complexity and positive-de nite requirement on the estimated covariance. We implement multivariate Gaussian regression through a Cholesky-based reparameterization of the covariance matrix. The distributional parameters|the means and the entries of the Cholesky factor|can be made to depend on covariates through exible additive predictors, allowing for nonlinear variations in mean and covariance. The reparameterization is compared to reference methods for estimating a xed covariance. An application for weather prediction (surface temperature) illustrates the exibility of the approach.