On the necessity of using imprecise probabilities for modelling environmental systems

One of the most important problems in the application of methods of parametric statistics to environmental systems is the impossibility of verifying the assumptions on probability distributions (e.g. the assumption of normally distributed measurements is usual but hardly exactly true). If Bayesian techniques are applied, the knowledge of probability distributions is even worse, because also vague prior knowledge (typical in modelling environmental systems) must be formulated in the form of (precise) prior probability distributions of model parameters or model structures. These two examples demonstrate the necessity of using imprecise probabilities in order to avoid arbitrariness in the choice of probability distributions. In spite of these well-known problems, imprecise probabilities are rarely used in environmental systems analysis and prediction. In order to motivate a change of this situation, this paper briefly reviews various techniques for the formulation of imprecise probabilities, and it demonstrates the advantages of using imprecise probabilities in a Bayesian context (for prior distributions and for measurement distributions) with a simple didactical example.