Bayesian Predictive Decision Synthesis: Methodology and Applications

Decision-guided perspectives on model uncertainty expand traditional statistical thinking about managing, comparing, and combining inferences from sets of models. In this dissertation, we present a novel framework entitled Bayesian predictive decision synthesis (BPDS) which advances conceptual and theoretical foundations in the intersection of model uncertainty and decision theory. We define new methodology that explicitly integrates decision-analytic outcomes into the evaluation, comparison and potential combination of candidate models. BPDS extends recent theoretical and practical advances based on both Bayesian predictive synthesis (BPS) and empirical goal-focused model uncertainty analysis. Specifically, we focus on the utilization of a specific outcome-dependent weight function in combination with more traditional model averaging methods that incorporate model performance. This outcome-dependent weight function is enabled by the development of a novel subjective Bayesian perspective on model weighting in predictive decision settings, with theoretical connections to Entropic Tilting and generalized Bayesian updating. We include multiple in-depth case studies from applied contexts to illustrate the use cases of BPDS and raise and investigate relevant questions. These case studies include applications in both the case where predictions depend on the decision at hand and the case where the decision has no impact on predictions. In the decision-dependent case, we present an optimal design for regression prediction and a collaboration involving macroeconomic forecasting. In the decision-independent case, we focus on a setting of sequential time series forecasting for financial portfolio decisions. Overall, these case studies are able to demonstrate the potential for BPDS to improve decisions and thus realized outcomes.