Speaker:  Spencer Wadsworth, PhD Candidate, Department of Statistics, Iowa State University

Title: Bayesian stacking via proper scoring rule optimization using a Gibbs posterior

Abstract:  In a probabilistic forecast hub, many researchers may collaborate and each submit their own forecasts of the same events. A forecast hub thus provides a locale where forecasts from the various participants may be assessed for skill, directly compared with other forecasts, and findings may be disseminated. Often, the forecasts in a forecast hub are combined into an ensemble forecast. A common method for combining forecasts is to construct an optimal linear pool where forecast distributions are weighted and summed into a mixture distribution. The selection of the model weights in a linear pool has received much attention and is often done by minimizing some score function or via Bayesian model averaging methods. Most methods either fail to provide uncertainty in their estimation of the weights or they do not cater well to problem specific needs. In this work we present the stacked Gibbs posterior (SGP), a novel method for combining forecasts by constructing an optimal linear pool via a Gibbs posterior. The weights of the linear pool are intended to optimize a proper scoring rule, which rule may be specified according to problem needs, and the Gibbs posterior allows for uncertainty quantification of the weights and regularization from a prior distribution. In two simulation studies, we compare the predictive performance of linear pool forecasts constructed using the SGP to linear pools constructed via Bayesian model averaging methods and an equally weighted pool. We also apply the SGP to forecasts from the 2023-24 CDC FluSight collaborative hub and compare the results to those of the model averaging and equally weighted methods. In each study, the forecasts from the SGP outperform ensemble forecasts from the other methods.