%0 Journal Article %1 Siegert2014 %A Siegert, Stefan %A Ferro, Christopher A. T. %A Stephenson, David B. %D 2014 %K IgnoranceScore LogarithmicScore RCM arxiv ensembles score %T Correcting the finite-ensemble bias of the Ignorance score %U http://arxiv.org/abs/1410.8249 %X This study considers the application of the Ignorance Score (also known as the Logarithmic Score) in the context of ensemble verification. In particular, we consider the case where an ensemble forecast is transformed to a Normal forecast distribution, and this distribution is evaluated by the Ignorance Score. It is shown that the Ignorance Score is biased with respect to the ensemble size, such that larger ensembles yield systematically better scores. A new estimator of the Ignorance score is derived which is unbiased with respect to the ensemble size, and thus allows for a fair comparison of ensembles of different sizes. In an application to seasonal climate predictions it is shown that the biased Ignorance score can assign better scores to large ensembles with poor quality than to small but skillful ensembles. By contrast, the new bias-corrected Ignorance score correctly ranks these ensembles according to their actual skill, independent of the number of members. It is shown that the unbiased estimator has smaller estimator variance and error than the biased estimator, and that it is a fair verification score, which is optimized if and only if the ensemble members are statistically consistent with the observations. A broader discussion is provided as to when a correction of the finite-ensemble bias of verification scores is actually desirable, and when it is not.

@article{Siegert2014, abstract = {This study considers the application of the Ignorance Score (also known as the Logarithmic Score) in the context of ensemble verification. In particular, we consider the case where an ensemble forecast is transformed to a Normal forecast distribution, and this distribution is evaluated by the Ignorance Score. It is shown that the Ignorance Score is biased with respect to the ensemble size, such that larger ensembles yield systematically better scores. A new estimator of the Ignorance score is derived which is unbiased with respect to the ensemble size, and thus allows for a fair comparison of ensembles of different sizes. In an application to seasonal climate predictions it is shown that the biased Ignorance score can assign better scores to large ensembles with poor quality than to small but skillful ensembles. By contrast, the new bias-corrected Ignorance score correctly ranks these ensembles according to their actual skill, independent of the number of members. It is shown that the unbiased estimator has smaller estimator variance and error than the biased estimator, and that it is a fair verification score, which is optimized if and only if the ensemble members are statistically consistent with the observations. A broader discussion is provided as to when a correction of the finite-ensemble bias of verification scores is actually desirable, and when it is not.}, added-at = {2014-11-07T15:30:56.000+0100}, author = {Siegert, Stefan and Ferro, Christopher A. T. and Stephenson, David B.}, biburl = {https://www.bibsonomy.org/bibtex/2d5bfb0d5565fd0f49b7eb02ddf37de5c/marsianus}, description = {[1410.8249] Correcting the finite-ensemble bias of the Ignorance score}, interhash = {cae03effcb3634a04ad4e5b488f8e1be}, intrahash = {d5bfb0d5565fd0f49b7eb02ddf37de5c}, keywords = {IgnoranceScore LogarithmicScore RCM arxiv ensembles score}, note = {cite arxiv:1410.8249Comment: 31 pages, 9 figures}, timestamp = {2014-11-07T15:30:56.000+0100}, title = {Correcting the finite-ensemble bias of the Ignorance score}, url = {http://arxiv.org/abs/1410.8249}, year = 2014 }