Decision criteria, data fusion and prediction calibration: a Bayesian approach

Abstract

The novel research paradigm, dubbed the “court of miracles of hydrological modelling”, focuses on achieving scientific progress in circumstances which traditionally would be called model failures. Many of the associated modelling issues can be addressed systematically and coherently within the mathematical framework of Bayesian forecast-decision theory. Five of them are addressed herein: (a) choosing a criterion function for making rational decisions under uncertainty (a meta-decision problem); (b) modelling stochastic dependence between variates to quantify uncertainty and predict realizations; (c) fusing data from asymmetric samples to cope with unrepresentativeness of small samples and corruptive effects of outliers; (d) calibrating probabilistic predictions against a prior distribution; and (e) ordering predictors, or models, in terms of their informativeness (equivalently, in terms of their economic value to a decider). It is suggested that communication between hydrologists and deciders (planners, engineers, operators of hydrosystems) would benefit if hydrologists adopted, at least on some issues, the perspective of deciders, who must act in a timely and rational manner, and for whom hydrological estimates and predictions have economic consequences.