Significance This paper compares the probabilistic accuracy of short-term forecasts of reported deaths due to COVID-19 during the first year and a half of the pandemic in the United States. Results show high variation in accuracy between and within stand-alone models and more consistent accuracy from an ensemble model that combined forecasts from all eligible models. This demonstrates that an ensemble model provided a reliable and comparatively accurate means of forecasting deaths during the COVID-19 pandemic that exceeded the performance of all of the models that contributed to it. This work strengthens the evidence base for synthesizing multiple models to support public-health action.

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We would like to thank Dome Wilson, Maria Harris, James Dykes, and Diane Sutherland for their valuable assistance on various aspects of this research.

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 multi-model ensemble forecast that combined predictions from dozens of different research 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-week horizon 3-5 times larger than when predicting at a 1-week 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. Significance Statement This paper compares the probabilistic accuracy of short-term forecasts of reported deaths due to COVID-19 during the first year and a half of the pandemic in the US. Results show high variation in accuracy between and within stand-alone models, and more consistent accuracy from an ensemble model that combined forecasts from all eligible models. This demonstrates that an ensemble model provided a reliable and comparatively accurate means of forecasting deaths during the COVID-19 pandemic that exceeded the performance of all of the models that contributed to it. This work strengthens the evidence base for synthesizing multiple models to support public health action.

Oxygen consumption, electroencephalogram (EEG), and four other measures of somatic relaxation were monitored in groups of long-term practitioners of classical Jacobson's progressive relaxation (PR) and Transcendental Meditation (TM) and also in a group of novice PR trainees. All subjects (1) practiced relaxation or meditation (treatment), (2) sat with eyes closed (EC control), and (3) read from a travel book during two identical sessions on different days. EEG findings indicated that all three groups remained primarily awake during treatment and EC control and that several subjects in each group displayed rare theta (5-7 Hz) waveforms. All three groups demonstrated similar decrements in somatic activity during treatment and EC control which were generally of small magnitude (e. g., 2-5% in oxygen consumption). These results supported the "relaxation response" model for state changes in somatic relaxation for techniques practiced under low levels of stress but not the claim that the relaxation response produced a hypometabolic state. Despite similar state effects, the long-term PR group manifested lower levels of somatic activity across all conditions compared to both novice PR and long-term TM groups. We concluded that PR causes a generalized trait of somatic relaxation which is manifested in a variety of settings and situations. Two likely explanations for this trait were discussed: (1) PR practitioners are taught to generalize relaxation to daily activities, and/or (2) according to a "multiprocess model," PR is a "somatic technique," which should produce greater somatic relaxation than does TM, a "cognitive technique." Further research is required to elucidate these possibilities.