Performance of the copula-based Morris Method

Abstract

The Morris method is a widely used screening method in sensitivity analysis. The method assumes that the input parameters are independent of each other. To overcome the assumption a copula-based Morris method is proposed. In this report the results of taking the dependencies into account are analyzed for the Morris method. For two examples sensitivity analysis is performed with the Morris method, with copula-based Morris method and by calculating sample correlations with a Monte Carlo simulation. From the analysis it follows that taking dependencies into account can have varying effects for different methods. It turns out that a straight-forward implementation makes the method often practically unusable. The sampling of model evaluation points becomes too computer expensive. The amount of copula evaluations is growing exponentially with the dimension and for copulas without an analytic expression these are already lengthy. The computational intensity can be reduced in two ways. First, one can approximate the probabilities. Different ways of approximating the probabilities are researched. Numerically integrating with the midpoint rule seems to be the best way of approximating the probabilities in the copula-based Morris method. Next to approximating the probabilities, one can also use the independent groups when implementing the method. When the input parameters are correlated there are usually a few groups of correlated parameters rather than that all the parameters are correlated with each other. This can be utilized to more efficiently implement the copula-based Morris method. When the group sizes are not increasing the computational intensity depends linearly instead of exponentially on the number of model parameters. By using both improvements the method can generally be applied to tens or hundreds of parameters in reasonable time, which is desired for a screening method.