Bayesian Decision Analysis and Constrained Forecasting
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A Bayesian decision analysis perspective on problems of constrained forecasting is presented and developed, motivated by increasing interest in problems of aggregate and hierarchical forecasting coupled with short-comings of traditional, purely inferential approaches. Foundational and pedagogic developments underlie new methodological approaches to such problems, explored and exemplified in contexts of total-constrained forecasting linked to motivating applications in commercial forecasting. The new perspective is complementary and integrated with traditional Bayesian inference approaches, while offering new practical methodology when the traditional view is challenged. Examples explore ranges of practically relevant loss functions in simple, illustrative contexts that highlight the opportunities for methodology as well as practically important questions of how constrained forecasting is impacted by dependencies among outcomes being predicted. The paper couples this core development with arguments in support of a broader view of Bayesian decision analysis than is typically adopted, involving studies of predictive distributions of loss function values under putative optimal decisions. Additional examples highlight the practical importance of this broader view in the constrained forecasting context. Extensions to more general constrained forecasting problems, and connections with broader interests in forecast reconciliation and aggregation are noted along with other broader considerations.
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