Conditioning multi-model ensembles for disease forecasting

Abstract

In this study we investigate how an ensemble of disease models can be conditioned to observational data, in a bid to improve its predictive skill. We use the ensemble of influenza forecasting models gathered by the US Centers for Disease Control and Prevention (CDC) as the exemplar. This ensemble is used every year to forecast the annual influenza outbreak in the United States. The models constituting this ensemble draw on very different modeling assumptions and approximations and are a diverse collection of methods to approximate epidemiological dynamics. Currently, each models' predictions are accorded the same importance, or weight, when compiling the ensemble's forecast. We consider this equally-weighted ensemble as the baseline case which has to be improved upon. In this study, we explore whether an ensemble forecast can be improved by "conditioning" the ensemble to whatever observational data is available from the ongoing outbreak. "Conditioning" can imply according the ensemble's members different weights which evolve over time, or simply perform the forecast using the top k (equally-weighted) models. In the latter case, the composition of the "top-k-see of models evolves over time. This is called "model averaging" in statistics. We explore four methods to perform model-averaging, three of which are new. We find that the CDC ensemble responds best to the "top-k-models" approach to model-averaging. All the new MA methods perform better than the baseline equally-weighted ensemble. The four model-averaging methods treat the models as black-boxes and simply use their forecasts as inputs i.e., one does not need access to the models at all, but rather only their forecasts. The model-averaging approaches reviewed in this report thus form a general framework for model-averaging any model ensemble.