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Combining probability forecasts

Author

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  • Roopesh Ranjan
  • Tilmann Gneiting
Abstract
Summary. Linear pooling is by far the most popular method for combining probability forecasts. However, any non‐trivial weighted average of two or more distinct, calibrated probability forecasts is necessarily uncalibrated and lacks sharpness. In view of this, linear pooling requires recalibration, even in the ideal case in which the individual forecasts are calibrated. Towards this end, we propose a beta‐transformed linear opinion pool for the aggregation of probability forecasts from distinct, calibrated or uncalibrated sources. The method fits an optimal non‐linearly recalibrated forecast combination, by compositing a beta transform and the traditional linear opinion pool. The technique is illustrated in a simulation example and in a case‐study on statistical and National Weather Service probability of precipitation forecasts.

Suggested Citation

  • Roopesh Ranjan & Tilmann Gneiting, 2010. "Combining probability forecasts," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(1), pages 71-91, January.
    • Handle: RePEc:bla:jorssb:v:72:y:2010:i:1:p:71-91
    DOI: 10.1111/j.1467-9868.2009.00726.x
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    References listed on IDEAS

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    1. Morris H. DeGroot & Julia Mortera, 1991. "Optimal Linear Opinion Pools," Management Science, INFORMS, vol. 37(5), pages 546-558, May.
    2. Mohamed N. Jouini & Robert T. Clemen, 1996. "Copula Models for Aggregating Expert Opinions," Operations Research, INFORMS, vol. 44(3), pages 444-457, June.
    3. Iversen, Edwin S & Parmigiani, Giovanni & Chen, Sining, 2008. "Multiple Model Evaluation Absent the Gold Standard Through Model Combination," Journal of the American Statistical Association, American Statistical Association, vol. 103(483), pages 897-909.
    4. Vladimir Vovk & Glenn Shafer, 2005. "Good randomized sequential probability forecasting is always possible," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(5), pages 747-763, November.
    5. Robert Winkler & Victor Jose, 2008. "Comments on: Assessing probabilistic forecasts of multivariate quantities, with an application to ensemble predictions of surface winds," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 17(2), pages 251-255, August.
    6. Tilmann Gneiting & Larissa Stanberry & Eric Grimit & Leonhard Held & Nicholas Johnson, 2008. "Rejoinder on: Assessing probabilistic forecasts of multivariate quantities, with an application to ensemble predictions of surface winds," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 17(2), pages 256-264, August.
    7. Tilmann Gneiting, 2008. "Editorial: Probabilistic forecasting," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 171(2), pages 319-321, April.
    8. Stephen C. Hora, 2004. "Probability Judgments for Continuous Quantities: Linear Combinations and Calibration," Management Science, INFORMS, vol. 50(5), pages 597-604, May.
    9. Robert L. Winkler & Roy M. Poses, 1993. "Evaluating and Combining Physicians' Probabilities of Survival in an Intensive Care Unit," Management Science, INFORMS, vol. 39(12), pages 1526-1543, December.
    10. Tilmann Gneiting & Fadoua Balabdaoui & Adrian E. Raftery, 2007. "Probabilistic forecasts, calibration and sharpness," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(2), pages 243-268, April.
    11. Dean Croushore, 1993. "Introducing: the survey of professional forecasters," Business Review, Federal Reserve Bank of Philadelphia, issue Nov, pages 3-15.
    12. Gneiting, Tilmann & Raftery, Adrian E., 2007. "Strictly Proper Scoring Rules, Prediction, and Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 359-378, March.
    13. Wallsten, Thomas S. & Diederich, Adele, 2001. "Understanding pooled subjective probability estimates," Mathematical Social Sciences, Elsevier, vol. 41(1), pages 1-18, January.
    14. Murphy, Allan H. & Winkler, Robert L., 1992. "Diagnostic verification of probability forecasts," International Journal of Forecasting, Elsevier, vol. 7(4), pages 435-455, March.
    15. Reinhard Selten, 1998. "Axiomatic Characterization of the Quadratic Scoring Rule," Experimental Economics, Springer;Economic Science Association, vol. 1(1), pages 43-61, June.
    16. Alvaro Sandroni & Rann Smorodinsky & Rakesh V. Vohra, 2003. "Calibration with Many Checking Rules," Mathematics of Operations Research, INFORMS, vol. 28(1), pages 141-153, February.
    17. Regnier, Eva, 2008. "Doing something about the weather," Omega, Elsevier, vol. 36(1), pages 22-32, February.
    18. Mary Kynn, 2008. "The ‘heuristics and biases’ bias in expert elicitation," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 171(1), pages 239-264, January.
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