Bayesian predictive decision synthesis.

This article introduces Bayesian Predictive Decision Synthesis (BPDS), a novel framework that extends traditional Bayesian model uncertainty analysis by explicitly integrating decision-analytic goals into the evaluation, comparison, and combination of predictive models. Building on Bayesian Predictive Synthesis (BPS) and empirical goal-focused model uncertainty methods, BPDS employs entropic tilting to reweight model predictions based on anticipated decision outcomes, thereby addressing model set incompleteness and improving decision-making under uncertainty. The methodology is illustrated through two applied examples: optimal experimental design in regression and sequential portfolio allocation using time-varying vector autoregressive models for financial returns. Results demonstrate that BPDS can yield more adaptive and effective decisions compared to standard Bayesian model averaging and adaptive variable selection, particularly by incorporating both predictive accuracy and decision-relevant utilities into model weighting. The article also discusses computational aspects, theoretical foundations, and potential extensions of BPDS for complex, multi-attribute decision problems in sequential time series contexts.