The Generation of Experimental Designs for Uncertainty and Sensitivity Analysis of Model Predictions with Emphasis on Dependences between Uncertain Parameters

One of the major steps of a probabilistic uncertainty and sensitivity analysis of model predictions is the generation of an experimental design, i.e. the selection of a multivariate sample of parameter values suitable to study the influence of parameter uncertainties on model predictions. In order to support the analyst in performing this task a computer program, named MEDUSA, has been written to generate the desired design after having received the necessary input data from the experts who are familiar with the various uncertain parameters. The paper presented describes the main features of this program.In MEDUSA two types of sample selection procedures are implemented: “simple random sampling” and “Latin Hypercube sampling”. The user can select from a set of several commonly used probability distributions for his uncertain parameters.In many practical cases some of the uncertain parameters cannot be regarded as independent and the problem arises how to express these dependences quantitatively and how to take them into account in the selection of the sample. Unlike the program in [1] MEDUSA offers for both design types two alternative methods to quantitatively express dependence between uncertain parameters. One of these methods, first introduced in ρ: ordinary correlation coefficientq: quadrant measureτ_K: Kendall’s τρ_S: Spearman’s pThese quantities are defined and interpreted in terms of population properties of bivariate distributions which seems to be more natural than a definition and interpretation in terms of empirical properties of bivariate samples.Additionally, MEDUSA contains a method to represent a kind of total dependence where there is some deterministic functional relationship between two parameters which complies with their marginal distributions.