Mixture distributions for probabilistic forecasts of disease outbreaks

TL;DR

This paper advocates for using discrete mixture distributions as a flexible, efficient, and comparable format for probabilistic disease outbreak forecasts in collaborative settings.

Contribution

It introduces the discrete mixture distribution format as a novel, practical alternative for probabilistic forecasting in collaborative disease outbreak modeling.

Findings

Discrete mixture distributions offer flexible shape modeling.

They simplify scoring and ensemble construction.

They require less storage than other formats.

Abstract

Collaboration among multiple teams has played a major role in probabilistic forecasting events of influenza outbreaks, the COVID-19 pandemic, other disease outbreaks, and in many other fields. When collecting forecasts from individual teams, ensuring that each team's model represents forecast uncertainty according to the same format allows for direct comparison of forecasts as well as methods of constructing multi-model ensemble forecasts. This paper outlines several common probabilistic forecast representation formats including parametric distributions, sample distributions, bin distributions, and quantiles and compares their use in the context of collaborative projects. We propose the use of a discrete mixture distribution format in collaborative forecasting in place of other formats. The flexibility in distribution shape, the ease for scoring and building ensemble models, and the reasonably low level of computer storage required to store such a forecast make the discrete mixture distribution an attractive alternative to the other representation formats.