Speaker: Spencer Wadsworth

Title: Stacking Probabilistic Forecasts via Gibbs Posterior Weight Optimization

Abstract: Combining probabilistic forecasts into a single ensemble forecast has become standard practice in collaborative forecast projects in many fields with linear pooling and quantile averaging being the most commonly used methods. A common idea is that weight selection methods should be tailored to the specific research question, and this has led to the use of selecting weights via optimization of proper scoring rules. Bayesian predictive synthesis has also emerged as a model probability updating scheme which provides a Bayesian solution to weight much more flexible than Bayesian model averaging. The various existing methods may or may not improve forecasting for any given dataset, and room for additional methodology may always exist. In this presentation, we introduce a Gibbs posterior on stacked model weights based on minimizing the continuous ranked probability score, a popular proper scoring rule. The Gibbs posterior extends model stacking into a more probabilistic framework by allowing for uncertainty quantification of weights and for optimal solutions to be influenced by a prior distribution. We provide a result on the posterior consistency of the stacked Gibbs posterior under the i.i.d. assumption. We also compare ensemble forecast performance with Bayesian model averaging, Bayesian predictive synthesis, and equal weighted models in a simulation study and on an example from the 2023-24 US Centers for Disease Control flu forecasting competition. In both the simulation and the real data analysis, the stacked Gibbs posterior outperforms the other methods herein.