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

TEST - Tập 17 Số 2 - Trang 211-235 - 2008
Tilmann Gneiting1, Larissa Stanberry1, Eric P. Grimit2, Leonhard Held3, Nicholas Johnson4
1Department of Statistics, University of Washington, Seattle, USA
23Tier Environmental Forecast Group, Seattle, USA
3Institut für Sozial- und Präventivmedizin, Abteilung Biostatistik, Universität Zürich, Zürich, Switzerland
4Department of Statistics, Stanford University, Stanford, USA

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Anderson JL (1996) A method for producing and evaluating probabilistic forecasts from ensemble model integrations. J Climate 9:1518–1525

Azzalini A, Genton MG (2008) Robust likelihood methods based on the skew-t and related distributions. Int Stat Rev 76:106–129

Bernardo JM (1979) Expected information as expected utility. Ann Stat 7:686–690

Berrocal VJ, Raftery AE, Gneiting T (2007) Combining spatial statistical and ensemble information in probabilistic weather forecasts. Mon Weather Rev 135:1386–1402

Besag J, Green P, Higdon D, Mengersen K (1995) Bayesian computing and stochastic systems. Stat Sci 10:3–66

Bickel PJ (1969) A distribution free version of the Smirnov two sample test in the p-variate case. Ann Math Stat 40:1–23

Bickel PJ, Lehmann EL (1979) Descriptive statistics for nonparametric models IV. Spread. In: Jureckova J (ed) Contributions to statistics. Academia, Prague, pp 33–40

Box GEP (1980) Sampling and Bayes’ inference in scientific modelling and robustness. J R Stat Soc Ser A 143:383–425

Brockwell AE (2007) Universal residuals: a multivariate transformation. Stat Probab Lett 77:1473–1478

Bröcker J, Smith LA (2007) Scoring probabilistic forecasts: the importance of being proper. Weather Forecast 22:382–388

Candille G, Talagrand O (2005) Evaluation of probabilistic prediction systems for a scalar variable. Q J R Meteorol Soc 131:2131–2150

Clements MP (2005) Evaluating econometric forecasts of economic and financial variables. Palgrave Macmillan, Basingstroke, Hampshire

Clements MP, Smith J (2000) Evaluating the forecast densities of linear and non-linear models: applications to output growth and unemployment. J Forecast 19:255–276

Clements MP, Smith J (2002) Evaluating multivariate forecast densities: a comparison of two approaches. Int J Forecast 18:397–407

Czado C, Gneiting T, Held L (2007) Predictive model assessment for count data. Tech Rep no 518, Dept of Statistics, University of Washington

Dawid AP (1984) Statistical theory: the prequential approach. J R Stat Soc Ser A 147:278–292

Dawid AP, Sebastiani P (1999) Coherent dispersion criteria for optimal experimental design. Ann Stat 27:65–81

De Gooijer JG (2007) Power of the Neyman smooth test for evaluating multivariate forecast densities. J Appl Stat 34:371–381

Delle Monache L, Hacker JP, Zhou Y, Deng X, Stull RB (2006) Probabilistic aspects of meteorological and ozone regional ensemble forecasts. J Geophys Res 111:D24307. doi: 10.1029/2005JD006917

Diebold FX, Mariano RS (1995) Comparing predictive accuracy. J Bus Econ Stat 13:253–263

Diebold FX, Gunther TA, Tay AS (1998) Evaluating density forecasts: with applications to financial risk management. Int Econ Rev 39:863–883

Diebold FX, Hahn J, Tay AS (1999) Multivariate density forecast evaluation and calibration in financial risk management: high-frequency returns on foreign exchange. Rev Econ Stat 81:661–673

Eckel FA, Mass CF (2005) Aspects of effective short-range ensemble forecasting. Weather Forecast 20:328–350

Friedman JH, Rafsky LC (1979) Multivariate generalizations of the Wald-Wolfowitz and Smirnov two-sample tests. Ann Stat 7:697–717

Genest C, Rivest LP (2001) On the multivariate probability integral transform. Stat Probab Lett 53:391–399

Gneiting T (2008) Editorial: probabilistic forecasting. J R Stat Soc Ser A 171:319–321

Gneiting T, Raftery AE (2005) Weather forecasting with ensemble methods. Science 310:248–249

Gneiting T, Raftery AE (2007) Strictly proper scoring rules, prediction, and estimation. J Am Stat Assoc 102:359–378

Gneiting T, Larson K, Westrick K, Genton MG, Aldrich E (2006) Calibrated probabilistic forecasting at the Stateline wind energy center: the regime-switching space-time (RST) method. J Am Stat Assoc 101:968–979

Gneiting T, Balabdaoui F, Raftery AE (2007) Probabilistic forecasts, calibration and sharpness. J R Stat Soc Ser B 69:243–268

Good IJ (1971) Comment on ‘Measuring information and uncertainty’ by Robert J. Buehler. In: Godambe VP, Sprott DA (eds) Foundations of statistical inference. Holt, Rinehart and Winston, Toronto, pp 337–339

Gombos D, Hansen JA, Du J, McQueen J (2007) Theory and applications of the minimum spanning tree rank histogram. Mon Weather Rev 135:1490–1505

Granger CWJ (2006) Preface: Some thoughts on the future of forecasting. Oxf Bull Econ Stat 67S:707–711

Grimit EP, Mass CF (2002) Initial results of a mesoscale short-range ensemble system over the Pacific Northwest. Weather Forecast 17:192–205

Grimit EP, Gneiting T, Berrocal VJ, Johnson NA (2006) The continuous ranked probability score for circular variables and its application to mesoscale forecast ensemble verification. Q J R Meteorol Soc 132:2925–2942

Hamill TM (1999) Hypothesis tests for evaluating numerical precipitation forecasts. Weather Forecast 14:155–167

Hamill TM (2001) Interpretation of rank histograms for verifying ensemble forecasts. Mon Weather Rev 129:550–560

Hamill TM, Colucci SJ (1997) Verification of Eta-RSM short-range ensemble forecasts. Mon Weather Rev 125:1312–1327

Hersbach H (2000) Decomposition of the continuous ranked probability score for ensemble prediction systems. Weather Forecast 15:559–570

Huber PJ (1985) Projection pursuit. Ann Stat 13:435–475

Ishida I (2005) Scanning multivariate conditional densities with probability integral transforms. Center for Advanced Research in Finance, University of Tokyo, Working Paper F-045

Jolliffe IT (2007) Uncertainty and inference for verification measures. Weather Forecast 22:637–650

Jolliffe IT, Stephenson DB (2003) Forecast verification: a practitioner’s guide in atmospheric science. Wiley, Chichester

Judd K, Smith LA, Weisheimer A (2007) How good is an ensemble at capturing truth? Using bounding boxes for forecast evaluation. Q J R Meteorol Soc 133:1309–1325

Kruskal JB (1956) On the shortest spanning subtree of a graph and the traveling salesman problem. Proc Am Math Soc 7:48–50

Krzysztofowicz R (2004) Bayesian processor of output: a new technique for probabilistic weather forecasting. In: Abstracts of the 17th conference on probability and statistics in the atmospheric sciences. Extended abstract no 4.2

Malmberg A, Holst J, Holst U (2008) A real-time assimilation algorithm applied to near-surface ocean wind fields. Environmetrics 19:319–330

Mass CF, Albright M, Ovens D, Steed R, MacIver M, Grimit E, Eckel T, Lamb B, Vaughan J, Westrick K, Storck P, Colman B, Hill C, Maykut N, Gilroy M, Ferguson SA, Yetter J, Sierchio JM, Bowman C, Stender R, Wilson R, Brown W (2003) Regional environmental prediction over the Pacific Northwest. Bull Am Meteorol Soc 84:1353–1366

Matheson JE, Winkler RL (1976) Scoring rules for continuous probability distributions. Manag Sci 22:1087–1096

Murphy AH, Winkler RL (1992) Diagnostic verification of probability forecasts. Int J Forecast 7:435–455

Murphy AH, Brown BG, Chen YS (1989) Diagnostic verification of temperature forecasts. Weather Forecast 4:485–501

National Research Council (2006) Completing the forecast: characterizing and communicating uncertainty for better decisions using weather and climate forecasts. The National Academies Press, Washington

O’Hagan A (2003) HSSS model criticism. In: Green PJ, Hjort NL, Richardson S (eds) Highly structured stochastic systems. Oxford University Press, Oxford, pp 423–444

Oja H (1983) Descriptive statistics for multivariate distributions. Stat Probab Lett 1:327–332

Oja H, Randles RH (2004) Multivariate nonparametric tests. Stat Sci 19:598–605

Palmer TN (2002) The economic value of ensemble forecasts as a tool for risk assessment: from days to decades. Q J R Meteorol Soc 128:747–774

Pepe MS (2003) The statistical evaluation of medical tests for classification and prediction. Oxford statistical science series, vol 28. Oxford University Press, Oxford

Raftery AE, Gneiting T, Balabdaoui F, Polakowski M (2005) Using Bayesian model averaging to calibrate forecast ensembles. Mon Weather Rev 133:1155–1174

Rife DL, Davis CA (2005) Verification of temporal variations in mesoscale numerical wind forecasts. Mon Weather Rev 133:3368–3381

Rosenblatt M (1952) Remarks on a multivariate transformation. Ann Math Stat 23:470–472

Roulston MS, Smith LA (2003) Combining dynamical and statistical ensembles. Tellus Ser A 55:16–25

Savage LJ (1971) Elicitation of personal probabilities and expectation. J Am Stat Assoc 66:783–801

Shaked M, Shanthikumar JG (1994) Stochastic orders and their applications. Academic, Boston

Shephard N (1994) Partial non-Gaussian state space. Biometrika 81:115–131

Smith LA (2001) Disentangling uncertainty and error: on the predictability of nonlinear systems. In: Mees AI (ed) Nonlinear dynamics and statistics. Birkhäuser, Boston, pp 31–64

Smith LA, Hansen JA (2004) Extending the limits of ensemble forecast verification with the minimum spanning tree histogram. Mon Weather Rev 132:1522–1528

Stephenson DB, Doblas-Reyes FJ (2000) Statistical methods for interpreting Monte Carlo forecasts. Tellus Ser A 52:300–322

Stigler SM (1975) The transition from point to distribution estimation. Bull Int Stat Inst 46:332–340

Talagrand O, Vautard R, Strauss B (1997) Evaluation of probabilistic prediction systems. In: Proceedings of a workshop held at ECMWF on predictability, 20–22 October 1997. European Centre for Medium-Range Weather Forecasts, Reading, pp 1–25

Timmermann A (2000) Density forecasting in economics and finance. J Forecast 19:231–234

Weisheimer A, Smith LA, Judd K (2005) A new view of seasonal forecast skill: bounding boxes from the DEMETER ensemble forecasts. Tellus Ser A 57:265–279

Wilks DS (2002) Smoothing forecast ensembles with fitted probability distributions. Q J R Meteorol Soc 128:2821–2836

Wilks DS (2004) The minimum spanning tree histogram as a verification tool for multidimensional ensemble forecasts. Mon Weather Rev 132:1329–1340

Wilks DS (2006) Statistical methods in the atmospheric sciences, 2nd edn. Elsevier Academic, Amsterdam

Wilson LJ, Burrows WR, Lanzinger A (1999) A strategy for verification of weather element forecasts from an ensemble prediction system. Mon Weather Rev 127:956–970

Winkler RL (1977) Rewarding expertise in probability assessment. In: Jungermann H, de Zeeuw G (eds) Decision making and change in human affairs. D. Reidel, Dordrecht, pp 127–140

Winkler RL (1996) Scoring rules and the evaluation of probabilities. Test 5:1–60

Zuo Y, Serfling R (2000) General notions of statistical depth functions. Ann Stat 28:461–482