Bayesian Forecasting. Roman Krzysztofowicz, University of Virginia
That forecasts should be stated in probabilistic rather than categorical terms has been argued from operational and decision-theoretic perspectives for almost a century. Yet most operational forecasts are deterministic and most research has been devoted to finding the "best" estimates rather than probability distributions of predictands. Undoubtedly, the leap from a deterministic frame of thought to one that not only admits our limited knowledge and information, but also quantifies uncertainty about future states, requires a coordinated effort at two levels: scientific—to build probabilistic forecast systems, and organizational—to alter the institutional mindset.
Bayesian theory offers both the rationale and the methods for probabilistic forecasting. Progress towards the applicability of Bayesian theory has been notable in three areas: (i) Bayesian Processor of Forecast—a procedure for post-processing deterministic forecasts from any sources in order to quantify the total uncertainty about a predictand. (ii) Bayesian Forecaster for Systems—a procedure for producing a probabilistic forecast of an output from a complex system whose model is imperfect and inputs are random. (iii) Judgmental assessment of multivariate distributions—the task usually complicated by the dimensionality and the nonlinearity of the stochastic dependence structure among variates. Recent applications in hydrometeorologic forecasting illustrate the appeal of the Bayesian framework and methods.