Screening: From tornado diagrams to effective dimensions

Popular sensitivity analysis techniques such as Tornado Diagrams or the Morris method are based on one-at-a-time input variations (local main effects, henceforth). We evidence a link between local main effects of screening methods and global sensitivity measures. The link allows analysts to obtain insights on interactions on the local and global scales simultaneously. We evidence a mirroring effect according to which a local main effect calculated from the base case to the sensitivity case is equal in magnitude to the local total effect in the opposite direction, and their difference yields an overall local interaction index. We then obtain the exact relationship between Morris sensitivity measures and Sobol’ total indices and discuss its implications on the choice of the sampling scheme. We show that the non-diagonal elements of the variance-covariance matrix of main effects computed at randomized locations yield Liu and Owen’s global interaction indices. Asymptotic results are derived with particular reference to confidence intervals for the mean dimension. We illustrate findings and insights through numerical experiments on two well known simulators.