Bayesian Forecasting via Deterministic Model

Rational decision making requires that the total uncertainty about a variate of interest (a predictand) be quantified in terms of a probability distribution, conditional on all available information and knowledge. Suppose the state-of-knowledge is embodied in a deterministic model, which is imperfect and outputs only an estimate of the predictand. Fundamentals are presented of two Bayesian methods for producing a probabilistic forecast via any deterministic model. The Bayesian Processor of Forecast (BPF) quantifies the total uncertainty in terms of a posterior distribution, conditional on model output. The Bayesian Forecasting System (BFS) decomposes the total uncertainty into input uncertainty and model uncertainty, which are characterized independently and then integrated into a predictive distribution. The BFS is compared with Monte Carlo simulation and ensemble forecasting technique, none of which can alone produce a probabilistic forecast that quantifies the total uncertainty, but each can serve as a component of the BFS.