Effect of uncertainty in input and parameter values on model prediction error

Uncertainty in input or parameter values affects the quality of model predictions. Uncertainty analysis attempts to quantify these effects. This is important, first of all as part of the overall investigation into model predictive quality and secondly in order to know if additional or more precise measurements are worthwhile. Here, two particular aspects of uncertainty analysis are studied. The first is the relationship of uncertainty analysis to the mean squared error of prediction (MSEP) of a model. It is shown that uncertainty affects the model bias contribution to MSEP, but this effect is only due to non linearities in the model. The direct effect of variability is on the model variance contribution to MSEP. It is shown that uncertainty in the input variables always increases model variance. Similarly, model variance is always larger when one averages over a range of parameter values, as compared with using the mean parameter values. However, in practice, one is usually interested in the model with specific parameter values. In this case, one cannot draw general conclusions in the absence of detailed assumptions about the correctness of the model. In particular, certain particular parameter values could give a smaller model variance than that given by the mean parameter values. The second aspect of uncertainty analysis that is studied is the effect on MSEP of having both literature-based parameters and parameters adjusted to data in the model. It is shown that the presence of adjusted parameters in general, decreases the effect of uncertainty in the literature parameters. To illustrate the theory derived here, we apply it to a model of sugar accumulation in fruit.