UNCERTAINTY ANALYSIS OF FOOD-CHAIN MODELS
Each sub-model has to be specified by a set of parameters, which are imperfectly known; it may also be influenced by unpredictable exogenous input. These uncertain inputs are collectively represented by the upward arrows in the diagram. The uncertainty about these inputs is often modelled by considering them as random variables.
The random effects propagate through the chain, by which some accumulation will occur. Uncertainty analysis provides methods to study the consequences of these random effects. The goal of such analyses is to evaluate if the joint effect on the final output y is still acceptably small, and to pinpoint the sources that contribute most to the uncertainty about the final output y. The results may be used to assess the potential benefits of control measures and of more accurate estimation of model parameters.
At present, most uncertainty analyses are performed computer-experimentally, by Monte Carlo methods. The model output is calculated for a representative sample of the uncertain model inputs. If the sample is large, the computational burden may be considerable. Several statistical methods have been developed to produce efficient Monte Carlo samples in order to keep the computational efforts as small as possible and to efficiently analyse the results. For a survey, see e.g. Helton (1993).
In Section 1, uncertainty and uncertainty contributions are characterised in terms of variances and variance components. Section 2 treats standard analyses based on regression-type approximations of the model output, the uncertain inputs serving as regressors. The analysis, which yields uncertainty contributions per individual input, is valid if the regression-approximation is of good quality. The approximation may fail because of non-linearities, especially in combination with a large number of inputs. Moreover, one may be interested in contributions of groups of inputs rather than individual inputs. Section 3 describes how, in such cases, one can have recourse to methods that are not based on regression-approximations, but that are more computer-intensive. Sections 2 and 3 contain examples of uncertainty analyses of models at the beginning of the food-chain. The paper ends with a discussion section.