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, 17:211 | Cite as

Assessing probabilistic forecasts of multivariate quantities, with an application to ensemble predictions of surface winds

  • Tilmann GneitingEmail author
  • Larissa I. Stanberry
  • Eric P. Grimit
  • Leonhard Held
  • Nicholas A. Johnson
Invited Paper

Abstract

We discuss methods for the evaluation of probabilistic predictions of vector-valued quantities, that can take the form of a discrete forecast ensemble or a density forecast. In particular, we propose a multivariate version of the univariate verification rank histogram or Talagrand diagram that can be used to check the calibration of ensemble forecasts. In the case of density forecasts, Box’s density ordinate transform provides an attractive alternative. The multivariate energy score generalizes the continuous ranked probability score. It addresses both calibration and sharpness, and can be used to compare deterministic forecasts, ensemble forecasts and density forecasts, using a single loss function that is proper. An application to the University of Washington mesoscale ensemble points at strengths and deficiencies of probabilistic short-range forecasts of surface wind vectors over the North American Pacific Northwest.

Keywords

Calibration Density forecast Ensemble postprocessing Exchangeability Forecast verification Probability integral transform Proper scoring rule Sharpness Rank histogram 

Mathematics Subject Classification (2000)

62H99 62P12 

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Copyright information

© Sociedad de Estadística e Investigación Operativa 2008

Authors and Affiliations

  • Tilmann Gneiting
    • 1
    Email author
  • Larissa I. Stanberry
    • 1
  • Eric P. Grimit
    • 2
  • Leonhard Held
    • 3
  • Nicholas A. Johnson
    • 4
  1. 1.Department of StatisticsUniversity of WashingtonSeattleUSA
  2. 2.3Tier Environmental Forecast GroupSeattleUSA
  3. 3.Institut für Sozial- und Präventivmedizin, Abteilung BiostatistikUniversität ZürichZürichSwitzerland
  4. 4.Department of StatisticsStanford UniversityStanfordUSA

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