Is It Better to Average Probabilities or Quantiles?

Lichtendahl, Kenneth C.; Grushka‐Cockayne, Yael; Winkler, Robert L.

doi:10.1287/mnsc.1120.1667

Cited by 125 publications

(98 citation statements)

References 30 publications

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“…Lichtendahl et al (2013) have examined averaging quantiles of continuous distributions given by multiple information sources rather than averaging probabilities. Both approaches of probability and quantile averaging have been applied in this paper for averaging the post-processed ensemble prediction system (EPS) based streamflow forecasts in order to get one predictive pdf or quantile forecast.…”

Section: Methodsmentioning

confidence: 99%

Technical note: Combining quantile forecasts and predictive distributions of streamflows

Bogner¹,

Liechti²,

Zappa³

2017

Hydrol. Earth Syst. Sci.

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Abstract. The enhanced availability of many different hydro-meteorological modelling and forecasting systems raises the issue of how to optimally combine this great deal of information. Especially the usage of deterministic and probabilistic forecasts with sometimes widely divergent predicted future streamflow values makes it even more complicated for decision makers to sift out the relevant information. In this study multiple streamflow forecast information will be aggregated based on several different predictive distributions, and quantile forecasts. For this combination the Bayesian model averaging (BMA) approach, the nonhomogeneous Gaussian regression (NGR), also known as the ensemble model output statistic (EMOS) techniques, and a novel method called Beta-transformed linear pooling (BLP) will be applied. By the help of the quantile score (QS) and the continuous ranked probability score (CRPS), the combination results for the Sihl River in Switzerland with about 5 years of forecast data will be compared and the differences between the raw and optimally combined forecasts will be highlighted. The results demonstrate the importance of applying proper forecast combination methods for decision makers in the field of flood and water resource management.

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Section: Methodsmentioning

confidence: 99%

Technical note: Combining quantile forecasts and predictive distributions of streamflows

Bogner¹,

Liechti²,

Zappa³

2017

Hydrol. Earth Syst. Sci.

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“…One method is based on averaging the quantiles of the 16 ensemble members directly, and the other one is calculated by averaging the probabilities derived from the approximated pdfs similar to the work of [76], which will be called QRNN-q-ave., respectively QRNN-p-ave.…”

Section: Modeling Implementationmentioning

confidence: 99%

Post-Processing of Stream Flows in Switzerland with an Emphasis on Low Flows and Floods

Bogner

Liechti

Zappa

2016

Water

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Post-processing has received much attention during the last couple of years within the hydrological community, and many different methods have been developed and tested, especially in the field of flood forecasting. Apart from the different meanings of the phrase "post-processing" in meteorology and hydrology, in this paper, it is regarded as a method to correct model outputs (predictions) based on meteorological (1) observed input data, (2) deterministic forecasts (single time series) and (3) ensemble forecasts (multiple time series) and to derive predictive uncertainties. So far, the majority of the research has been related to floods, how to remove bias and improve the forecast accuracy and how to minimize dispersion errors. Given that global changes are driving climatic forces, there is an urgent need to improve the quality of low-flow predictions, as well, even in regions that are normally less prone to drought. For several catchments in Switzerland, different post-processing methods were tested with respect to low stream flow and flooding conditions. The complexity of the applied procedures ranged from simple AR processes to more complex methodologies combining wavelet transformations and Quantile Regression Neural Networks (QRNN) and included the derivation of predictive uncertainties. Furthermore, various verification methods were tested in order to quantify the possible improvements that could be gained by applying these post-processing procedures based on different stream flow conditions. Preliminary results indicate that there is no single best method, but with an increase of complexity, a significant improvement of the quality of the predictions can be achieved.

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“…Averaging quantiles is a common students' mistake when trying to compute the average of experts' distributions, but it has also been promoted in its own right (Lichtendahl et al 2013), without checking its performance on real expert data. It appears to have eluded many that averaging quantiles is equivalent to harmonically weighting the experts' densities.…”

Section: Consensus Distributionmentioning

confidence: 99%

A commentary on “how to interpret expert judgment assessments of twenty-first century sea-level rise” by Hylke de Vries and Roderik SW van de Wal

2016

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We clarify key aspects of the evaluation, by de Vries and van de Wal (2015), of our expert elicitation paper on the contributions of ice sheet melting to sea level rise due to future global temperature rise scenarios (Bamber and Aspinall 2013), and extend the conversation with further analysis of their proposed approach for combining expert uncertainty judgments. Aspinall (2013: [BA13]), and welcome this opportunity to clarify the work presented in BA13 and extend the analysis of VW15. The problem of finding a science-based quantification of uncertainty for poorly constrained physical models with large societal impacts deserves high priority in the climate community. This entails crossing discipline boundaries and will take that community outside its usual scientific comfort zone. We therefore salute the authors of VW13 for venturing into this alien terrain and welcome the opportunity to address some of the issues they raise. We thank de Vries and van de Wal (2015: [VW15]) for their detailed consideration of Bamber andThe present commentary discusses certain important and unique attributes of BA13's expert weighting scheme that are misinterpreted in VW15, then addresses the Bconsensus distributionô f VW15, their Blevel of consensus^, and the issue of lognormal fitting elicited data.1 Weighting scheme VW15 state: BThe answers of the experts [in BA13] were weighted using a specialised weighting technique, which involved the self-estimated level of expertise and confidence of the respondents^.

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Is It Better to Average Probabilities or Quantiles?

Cited by 125 publications

References 30 publications

Technical note: Combining quantile forecasts and predictive distributions of streamflows

Technical note: Combining quantile forecasts and predictive distributions of streamflows

Post-Processing of Stream Flows in Switzerland with an Emphasis on Low Flows and Floods

A commentary on “how to interpret expert judgment assessments of twenty-first century sea-level rise” by Hylke de Vries and Roderik SW van de Wal

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