A Stochastic Approach to Model Uncertainty

Fedra, K. (1979). A Stochastic Approach to Model Uncertainty. IIASA Working Paper. IIASA, Laxenburg, Austria: WP-79-063

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Abstract

A stochastic approach for modeling uncertain and incompletely known ecosystems, using a lake modeling example, is proposed. In order to estimate the reliability and precision of model predictions based on uncertain data from ecological systems, the explicit inclusion of the uncertainty in the numerical modeling approach is advocated. Starting with a fuzzy definition of systems behavior in terms of a behaviour space region, the corresponding region in the data space of a given model is explored by Monte Carlo techniques. A set of data vectors -- random samples from the data space region corresponding to the empirical range of systems behaviour -- is then used to generate independent estimates of states or outputs for selected deterministic inputs. These estimates have to be understood as random samples from a probabilistic behaviour space which reflects the initial uncertainty in data space delimitation. The estimates are used to establish probability distributions for systems states or outputs (cross-sections of the probabilistic behaviour space) for the given input conditions. These probability distributions replace the deterministic point-estimates of a traditional approach, and reflect the incomplete knowledge about the system as well as the stochastic variability of ecosystems. The approach is extended for long-term simulations of systems behavior under changed input conditions, and estimates of prediction accuracy in time are obtained.

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