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1. Blended Probabilistic Tornado Forecasts: Combining Climatological Frequencies with NSSL–WRF Ensemble Forecasts

   https://doi.org/10.1175/WAF-D-17-0132.1  

   Gallo, Burkely T. ; Clark, Adam J. ; Smith, Bryan T. ; Thompson, Richard L. ; Jirak, Israel ; Dembek, Scott R. ( April 2018 , Weather and Forecasting)
2. Evaluation of individual and ensemble probabilistic forecasts of COVID-19 mortality in the United States

   https://doi.org/10.1073/pnas.2113561119  

   Cramer, Estee Y. ; Ray, Evan L. ; Lopez, Velma K. ; Bracher, Johannes ; Brennen, Andrea ; Castro Rivadeneira, Alvaro J. ; Gerding, Aaron ; Gneiting, Tilmann ; House, Katie H. ; Huang, Yuxin ; et al ( April 2022 , Proceedings of the National Academy of Sciences)

   Short-term probabilistic forecasts of the trajectory of the COVID-19 pandemic in the United States have served as a visible and important communication channel between the scientific modeling community and both the general public and decision-makers. Forecasting models provide specific, quantitative, and evaluable predictions that inform short-term decisions such as healthcare staffing needs, school closures, and allocation of medical supplies. Starting in April 2020, the US COVID-19 Forecast Hub ( https://covid19forecasthub.org/ ) collected, disseminated, and synthesized tens of millions of specific predictions from more than 90 different academic, industry, and independent research groups. A multimodel ensemble forecast that combined predictions from dozens of groups every week provided the most consistently accurate probabilistic forecasts of incident deaths due to COVID-19 at the state and national level from April 2020 through October 2021. The performance of 27 individual models that submitted complete forecasts of COVID-19 deaths consistently throughout this year showed high variability in forecast skill across time, geospatial units, and forecast horizons. Two-thirds of the models evaluated showed better accuracy than a naïve baseline model. Forecast accuracy degraded as models made predictions further into the future, with probabilistic error at a 20-wk horizon three to five times larger than when predicting at a 1-wk horizon. This project underscores the role that collaboration and active coordination between governmental public-health agencies, academic modeling teams, and industry partners can play in developing modern modeling capabilities to support local, state, and federal response to outbreaks. 

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3. Evaluation of individual and ensemble probabilistic forecasts of COVID-19 mortality in the US.

   https://doi.org/10.1101/2021.02.03.21250974  

   Cramer, E.Y. ( January 2022 , Proceedings of the National Academy of Sciences of the United States of America)
4. Evaluation of individual and ensemble probabilistic forecasts of COVID-19 mortality in the United States

   https://doi.org/10.1073/211356111  

   Cramer, E.Y. ; Ray, E.L. ; Lopez, V.K. ; Bracher, J. ; Brennen, A. ; Castro Rivadeneira, A.J. ; Gerding, A. ; Gneiting, T. ; House, K.H. ; Huang, Y. ; et al ( January 2022 , Proceedings of the National Academy of Sciences of the United States of America)
5. Probabilistic Forecasts of Wind Speed: Ensemble Model Output Statistics by using Heteroscedastic Censored Regression

   https://doi.org/10.1111/j.1467-985X.2009.00616.x  

   Thorarinsdottir, Thordis L. ; Gneiting, Tilmann ( November 2009 , Journal of the Royal Statistical Society Series A: Statistics in Society)

   As wind energy penetration continues to grow, there is a critical need for probabilistic forecasts of wind resources. In addition, there are many other societally relevant uses for forecasts of wind speed, ranging from aviation to ship routing and recreational boating. Over the past two decades, ensembles of dynamical weather prediction models have been developed, in which multiple estimates of the current state of the atmosphere are used to generate a collection of deterministic forecasts. However, even state of the art ensemble systems are uncalibrated and biased. Here we propose a novel way of statistically post-processing dynamical ensembles for wind speed by using heteroscedastic censored (tobit) regression, where location and spread derive from the ensemble. The resulting ensemble model output statistics method is applied to 48-h-ahead forecasts of maximum wind speed over the North American Pacific Northwest by using the University of Washington mesoscale ensemble. The statistically post-processed density forecasts turn out to be calibrated and sharp, and result in a substantial improvement over the unprocessed ensemble or climatological reference forecasts.

    

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