Extending Extended Logistic Regression: Extended versus Separate versus Ordered versus Censored

AbstractExtended logistic regression is a recent ensemble calibration method that extends logistic regression to provide full continuous probability distribution forecasts. It assumes conditional logistic distributions for the (transformed) predictand and fits these using selected predictand category probabilities. In this study extended logistic regression is compared to the closely related ordered and censored logistic regression models. Ordered logistic regression avoids the logistic distribution assumption but does not yield full probability distribution forecasts, whereas censored regression directly fits the full conditional predictive distributions. The performance of these and other ensemble postprocessing methods is tested on wind speed and precipitation data from several European locations and ensemble forecasts from the European Centre for Medium-Range Weather Forecasts (ECMWF). Ordered logistic regression performed similarly to extended logistic regression for probability forecasts of discrete...

[1]  M. Scheuerer.  Probabilistic quantitative precipitation forecasting using Ensemble Model Output Statistics , 2013, 1302.0893.

[2]  Leonard A. Smith,et al.  Combining dynamical and statistical ensembles , 2003 .

[3]  Edward S. Epstein,et al.  A Scoring System for Probability Forecasts of Ranked Categories , 1969 .

[4]  J. Tobin.  Estimation of Relationships for Limited Dependent Variables , 1958 .

[5]  J. Ruiz,et al.  How sensitive are probabilistic precipitation forecasts to the choice of calibration algorithms and the ensemble generation method? Part I: sensitivity to calibration methods , 2012 .

[6]  P. McCullagh,et al.  Generalized Linear Models , 1984 .

[7]  M. Schmeits,et al.  A Comparison between Raw Ensemble Output, (Modified) Bayesian Model Averaging, and Extended Logistic Regression Using ECMWF Ensemble Precipitation Reforecasts , 2010 .

[8]  Xuguang Wang,et al.  A Comparison of Breeding and Ensemble Transform Kalman Filter Ensemble Forecast Schemes , 2003 .

[9]  P. McCullagh,et al.  Generalized Linear Models , 1972, Predictive Analytics.

[10]  Daniel S. Wilks,et al.  Comparison of ensemble‐MOS methods in the Lorenz '96 setting , 2006 .

[11]  Z. B. Bouallègue.  Calibrated Short-Range Ensemble Precipitation Forecasts Using Extended Logistic Regression with Interaction Terms , 2013 .

[12]  H. Hersbach.  Decomposition of the Continuous Ranked Probability Score for Ensemble Prediction Systems , 2000 .

[13]  Thomas M. Hamill,et al.  Comparison of Ensemble-MOS Methods Using GFS Reforecasts , 2007 .

[14]  A. Agresti.  Categorical data analysis , 1993 .

[15]  A. Raftery,et al.  Using Bayesian Model Averaging to Calibrate Forecast Ensembles , 2005 .

[16]  T. Gneiting,et al.  Uncertainty Quantification in Complex Simulation Models Using Ensemble Copula Coupling , 2013, 1302.7149.

[17]  Tilmann Gneiting,et al.  Probabilistic forecasts of wind speed: ensemble model output statistics by using heteroscedastic censored regression , 2010 .

[18]  Leonard A. Smith,et al.  Increasing the Reliability of Reliability Diagrams , 2007 .

[19]  Eric R. Ziegel,et al.  Generalized Linear Models , 2002, Technometrics.

[20]  Daniel S. Wilks,et al.  Extending logistic regression to provide full‐probability‐distribution MOS forecasts , 2009 .

[21]  R. L. Winkler,et al.  Scoring Rules for Continuous Probability Distributions , 1976 .

[22]  Emmanuel Roulin,et al.  Postprocessing of Ensemble Precipitation Predictions with Extended Logistic Regression Based on Hindcasts , 2012 .

[23]  Thomas M. Hamill,et al.  Verification of TIGGE Multimodel and ECMWF Reforecast-Calibrated Probabilistic Precipitation Forecasts over the Contiguous United States* , 2012 .

[24]  J. Whitaker,et al.  Ensemble Forecasts and the Properties of Flow-Dependent Analysis-Error Covariance Singular Vectors , 2003 .

[25]  Thomas M. Hamill,et al.  Ensemble Reforecasting: Improving Medium-Range Forecast Skill Using Retrospective Forecasts , 2004 .

[26]  Anton H. Westveld,et al.  Calibrated Probabilistic Forecasting Using Ensemble Model Output Statistics and Minimum CRPS Estimation , 2005 .

[27]  Achim Zeileis,et al.  Heteroscedastic Extended Logistic Regression for Postprocessing of Ensemble Guidance , 2014 .