Monte Carlo Estimation of Uncertainty Contributions from Several Independent Multivariate Sources

Summary

An efficient random sampling method is introduced to estimate the contributions of several sources of uncertainty to prediction variance of (computer) models. Prediction uncertainty is caused by uncertainty about the initial state, parameters, unknown (e.g. future) exogenous variables, noises, etcetera. Such uncertainties are modelled here as random inputs into a deterministic model, which translates input uncertainty into output uncertainty. The goal is to pinpoint the major causes of output uncertainty. The method presented is particularly suitable for cases where uncertainty is present in a large number of inputs (such as future weather conditions). The expected reduction of output variance is estimated for the case that various (groups of) inputs should become fully determined. The method can be applied if the input sources fall into stochastically independent groups. The approach is more flexible than conventional methods based on approximations of the model. An agronomic example illustrates the method. A deterministic model is used to advise farmers on control of brown rust in wheat. Empirical data were used to estimate the distributions of uncertain inputs. Analysis shows that effective improvement of the precision of the model’s prediction requires alternative submodels describing pest population dynamics, rather than better determination of initial conditions and parameters.