Probabilistic Forecasting

Posted: 7 Mar 2014

See all articles by Tilmann Gneiting

Tilmann Gneiting

University of Washington - Department of Statistics and Biostatistics

Matthias Katzfuss

Texas A&M University - Department of Statistics

Date Written: January 2014

Abstract

A probabilistic forecast takes the form of a predictive probability distribution over future quantities or events of interest. Probabilistic forecasting aims to maximize the sharpness of the predictive distributions, subject to calibration, on the basis of the available information set. We formalize and study notions of calibration in a prediction space setting. In practice, probabilistic calibration can be checked by examining probability integral transform (PIT) histograms. Proper scoring rules such as the logarithmic score and the continuous ranked probability score serve to assess calibration and sharpness simultaneously. As a special case, consistent scoring functions provide decision-theoretically coherent tools for evaluating point forecasts. We emphasize methodological links to parametric and nonparametric distributional regression techniques, which attempt to model and to estimate conditional distribution functions; we use the context of statistically postprocessed ensemble forecasts in numerical weather prediction as an example. Throughout, we illustrate concepts and methodologies in data examples.

Suggested Citation

Gneiting, Tilmann and Katzfuss, Matthias, Probabilistic Forecasting (January 2014). Annual Review of Statistics and Its Application, Vol. 1, Issue 1, pp. 125-151, 2014. Available at SSRN: https://ssrn.com/abstract=2405902 or http://dx.doi.org/10.1146/annurev-statistics-062713-085831

Tilmann Gneiting (Contact Author)

University of Washington - Department of Statistics and Biostatistics ( email )

Seattle, WA
United States

Matthias Katzfuss

Texas A&M University - Department of Statistics ( email )

155 Ireland Street
447 Blocker
College Station, TX 77843
United States

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