Why should a forecaster and a decision maker use Bayes Theorem

Forecasts of hydrometeorologic phenomena are inherently uncertain. In practice, uncertainty is often ignored. To aid forecasters and decision makers in coping with forecast uncertainty, we investigate theoretical and exemplary answers to several fundamental questions: How to optimally use categorical and probabilistic forecasts? What opportunity losses are expected to be incurred when forecast uncertainty is ignored? Why the classical contingency analysis is suboptimal? What economic gains are to be expected from probabilistic forecasts? To illuminate the answers, analytic solutions are derived for the optimal and a nonoptimal (one that ignores forecast uncertainty) formulation of a single‐period quadratic decision problem with a categorical and probabilistic forecast of the state. The probabilistic forecast is of the type wherein the forecaster quantifies his degree of uncertainty in terms of a fixed‐probability central credible interval. Bayesian information processors for forecasts of normally distributed state variables are formulated by using conjugate families of distributions and are applied to records of daily temperature forecasts.