4.6
Conditional Dependence and Sufficient Statistics of an Ensemble
Roman Krzysztofowicz, University of Virginia, Charlottesville, VA
The Bayesian Processor of Ensemble (BPE) is a new, theoretically-based technique for probabilistic forecasting of weather variates. It processes an ensemble of estimates output from a numerical weather prediction (NWP) model and optimally fuses it with climatic data in order to quantify uncertainty about a predictand in the form of a posterior distribution function. In principle, the posterior distribution function is conditional on all ensemble members, which enter the BPE via a likelihood function. The meta-Gaussian family of likelihood functions is employed to allow all forms of marginal distribution functions, and non-linear and heteroscedastic dependence structures. Two modeling challenges remain. (i) To reduce the complexity of the family of likelihood functions without making arbitrary assumptions and thus without loosing any predictive information contained in the ensemble, it is necessary to identify the conditional dependence structure of the ensemble. (ii) To reduce the dimensionality of the conditioning without losing any predictive information, it is necessary to identify sufficient statistics of the ensemble.
This talk will report results of an empirical investigation into both hypotheses. The investigation was performed on a sample of ensemble forecasts of temperature at 1200 UTC produced with lead times of 12–156 h during 12 months (1 January 2005 – 31 December 2005) at the National Centers for Environmental Prediction. The results strongly support both hypotheses: (i) That the ensemble has a reduced dependence structure albeit the ensemble members are not conditionally independent (and thus do not constitute a random sample). (ii) That a few summary statistics are as informative as the entire ensemble.
Session 4, Ensemble Forecasting Including Post Processing IV
Monday, 21 January 2008, 4:00 PM-5:30 PM, 219
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