On the Relationship Between the Sensitivity Measures Proposed by Morris and the Variance Based Measures

摘要

A variety of methods have been proposed in the literature to perform sensitivity analysis on a model. Each method has its advantages and disadvantages. The choice of which sensitivity method to adopt depends on the objective of the analysis, i.e. on the question that the analyst is addressing, on the properties of the model under study (e.g.. model linearity, monotonicity, etc.), and on the computational effort required for each model evaluation. In this work we assume that the aim of the analysis is to identify those input factors that are irrelevant in the model, i.e. those factors that can be fixed to any value within their range of variation without significantly affecting the output variance. This problem is known in the literature as the problem of Factor Fixing, but it can also be denoted as a problem of screening, where the goal is to screen a few important factors among a large number contained in a model. A class of methods that has shown to perform well in this setting is that of the so-called variance based methods, also known as importance measures or sensitivity indices. Variance based techniques have several desirable properties. They are "model free", in the sense that they are independent of assumptions about the model such as linearity, additivity and so on. They are "global", i.e. they explore the entire interval of definition of each factor and the effect of each factor is taken as an average over the possible values of the other factors. They are usually "quantitative", which is they can tell how much factor a is more important than factor b.