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Probabilistic forecasts, calibration and sharpness

Gneiting, Tilmann; Balabdaoui, Fadoua; Raftery, Adrian E. (2007), Probabilistic forecasts, calibration and sharpness, Journal of the Royal Statistical Society. Series B, Statistical Methodology, 69, 2, p. 243-268. http://dx.doi.org/10.1111/j.1467-9868.2007.00587.x

Type
Article accepté pour publication ou publié
External document link
http://hal.archives-ouvertes.fr/hal-00363242/en/
Date
2007
Journal name
Journal of the Royal Statistical Society. Series B, Statistical Methodology
Volume
69
Number
2
Publisher
Blackwell Publishing
Pages
243-268
Publication identifier
http://dx.doi.org/10.1111/j.1467-9868.2007.00587.x
Metadata
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Author(s)
Gneiting, Tilmann

Balabdaoui, Fadoua

Raftery, Adrian E.
Abstract (EN)
Probabilistic forecasts of a continuous variable take the form of predictive densities or predictive cumulative distribution functions. We propose a diagnostic approach to the evaluation of predictive performance that is based on the paradigm of {\sl maximizing the sharpness of the predictive distributions subject to calibration}. Calibration refers to the statistical consistency between the distributional forecasts and the observations and is a joint property of the predictions and the events that materialize. Sharpness refers to the concentration of the predictive distributions and is a property of the forecasts only. A simple theoretical framework phrased in terms of a game between nature and forecaster allows us to distinguish probabilistic calibration, exceedance calibration and marginal calibration. We propose and study tools for checking calibration and sharpness, among them the probability integral transform (PIT) histogram, marginal calibration plots, the sharpness diagram and proper scoring rules. The diagnostic approach is illustrated by an assessment and ranking of probabilistic forecasts of wind speed at the Stateline wind energy center in the U.S.~Pacific Northwest. In combination with cross-validation or in the time series context, our proposal provides very general, nonparametric alternatives to the use of information criteria for model diagnostics and model selection.
Subjects / Keywords
Proper scoring rule; Probability integral transform; Prequential principle; Predictive distribution; Posterior predictive assessment; Model diagnostics; Forecast verification; Ex post evaluation; Ensemble prediction system; Density forecast; Cross-validation

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