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Prediction intervals for Poisson‐based regression models

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Abstract This paper provides a review of the literature regarding methods for constructing prediction intervals for counting variables, with particular focus on those whose distributions are Poisson or derived from Poisson and with an over‐dispersion property. Independent and identically distributed models and regression models are both considered. The motivating problem for this review is that of predicting the number of daily and cumulative cases or deaths attributable to COVID‐19 at a future date. This article is categorized under: Applications of Computational Statistics > Clinical Trials Statistical Learning and Exploratory Methods of the Data Sciences > Modeling Methods Statistical Models > Generalized Linear Models
Reported daily direct COVID‐19 deaths for the United States from March 1 to December 14, 2020. Three subregions are split by dashed‐lines and indicate the first, second, and third waves. The thresholds, July 5, and October 14, are the points with the minimum 7‐day rolling average deaths in the valleys
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Point predictions and prediction intervals of the cumulative deaths attributed to COVID‐19 during the first, second, and third waves based on three approaches. (a) Prediction periods in United States cumulative deaths due to COVID‐19, (b) predictions during the first wave, (c) predictions during the second wave, (d) predictions during the third wave
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Statistical Models > Generalized Linear Models
Statistical Learning and Exploratory Methods of the Data Sciences > Modeling Methods
Applications of Computational Statistics > Clinical Trials

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