Interaction Effects in Subinterval Sensitivity Analysis

This paper expands upon subinterval sensitivity by considering the simultaneous effect of pairs and triplets of variables at the same time. We assert that individual subinterval sensitivity indices quantify interaction effects and thus they can be regarded as full-blown global sensitivity indices. We consider simultaneous effects only as a means to show the global character of individual indices. In fact, the calculation of simultaneous effects is used as a diagnostic tool to detect the presence and extent of interaction effects. This confirms our proposition that individual subinterval indices are indeed comparable to Sobol’ total indices. It turns out that when there are interaction effects the individual indices lose "additivity", meaning that their sum is never equal to their corresponding simultaneous indices. In particular, we find that simultaneous indices are always smaller than the sum of the individual first-order indices in the presence of interaction effects. Moreover, we find that the exact opposite is true also: When the first-order indices add up exactly to their corresponding simultaneous index there are no interaction effects. This method can be very cheap in determining interaction effects because only a small number of subintervals (e.g. five) are needed. In the absence of interaction effects, the difference between the sum of first-order indices and their corresponding simultaneous index can also quantify the effect of inflation due to repeated variables within a function. The caveat is that the conflated presence of inflation and interaction effects within a mathematical model contaminates the results, making it difficult to discern between the two effects and in turns adding artefactual uncertainty on the sensitivity indices. This motivates the need to develop ways of removing or mitigating inflation of interval computation to ensure that reliable results are obtained.

Keywords: Sensitivity analysis, Interaction effects, Interval computation, Subinterval sensitivity.