The quality of precipitation forecasts is difficult to evaluate objectively because images with disjointed features surrounded by zero intensities cannot easily be compared pixel by pixel: any displacement between observed and predicted fields is punished twice, generally leading to better marks for coarser models. To answer the question of whether a highly resolved model truly delivers an improved representation of precipitation processes, alternative tools are thus needed. Wavelet transformations can be used to summarize high-dimensional data in a few numbers which characterize the field's texture. A comparison of the transformed fields judges models solely based on their ability to predict spatial structures. The fidelity of the forecast's overall pattern is thus investigated separately from potential errors in feature location. This study introduces several new waveletbased structure scores for the verification of deterministic as well as ensemble predictions. Their properties are rigorously tested in an idealized setting: a recently developed stochastic model for precipitation extremes generates realistic pairs of synthetic observations and forecasts with prespecified spatial correlations. The wavelet scores are found to react sensitively to differences in structural properties, meaning that the objectively best forecast can be determined even in cases where this task is difficult to accomplish by naked eye. Random rain fields prove to be a useful test bed for any verification tool that aims for an assessment of structure.Published by Copernicus Publications on behalf of the European Geosciences Union.

Abstract. The quality of precipitation forecasts is difficult to evaluate objectively because images with disjoint features surrounded by zero intensities cannot easily be compared pixel by pixel: Any displacement between observed and predicted field is punished twice, generally leading to better marks for coarser models. To answer the question whether a highly resolved model truly delivers an improved representation of precipitation processes, alternative tools are thus needed. Wavelet transformations can be used to summarize high-dimensional data in a few numbers which characterize the field's texture. A comparison of the transformed fields judges models solely based on their ability to predict spatial correlations. The fidelity of the forecast's overall structure is thus investigated separately from potential errors in feature location. This study introduces several new wavelet based structure-scores for the verification of deterministic as well as ensemble predictions. Their properties are rigorously tested in an idealized setting: A recently developed stochastic model for precipitation extremes generates realistic pairs of synthetic observations and forecasts with prespecified spatial correlations. The wavelet-scores are found to react sensitively to differences in structural properties, meaning that the objectively best forecast can be determined even in cases where this task is difficult to accomplish by naked eye. Random rain fields prove to be a useful test-bed for any verification tool that aims for an assessment of structure.

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We investigate the application of ensemble transform approaches to Bayesian inference of logistic regression problems. Our approach relies on appropriate extensions of the popular ensemble Kalman filter and the feedback particle filter to the cross entropy loss function and is based on a well-established homotopy approach to Bayesian inference. The arising finite particle evolution equations as well as their mean-field limits are affine-invariant. Furthermore, the proposed methods can be implemented in a gradient-free manner in case of nonlinear logistic regression and the data can be randomly subsampled similar to mini-batching of stochastic gradient descent. We also propose a closely related SDE-based sampling method which again is affine-invariant and can easily be made gradient-free. Numerical examples demonstrate the appropriateness of the proposed methodologies.

We investigate the application of ensemble transform approaches to Bayesian inference of logistic regression problems. Our approach relies on appropriate extensions of the popular ensemble Kalman filter and the feedback particle filter to the cross entropy loss function and is based on a well-established homotopy approach to Bayesian inference. The arising finite particle evolution equations as well as their mean-field limits are affine-invariant. Furthermore, the proposed methods can be implemented in a gradient-free manner in case of nonlinear logistic regression and the data can be randomly subsampled similar to mini-batching of stochastic gradient descent. We also propose a closely related SDE-based sampling method which again is affine-invariant and can easily be made gradient-free. Numerical examples demonstrate the appropriateness of the proposed methodologies.