Local probabilistic sensitivity measures for comparing FORM and Monte Carlo calculations illustrated with dike ring reliability calculations Original Research Article

We define local probabilistic sensitivity measures as proportional to ∂E(Xi|Z = z)/∂z, where Z is a function of random variables XI,…,Xn. These measures are local in that they depend only on the neighborhood of Z = z, but unlike other local sensitivity measures, the local probabilistic sensitivity of Xi does not depend on values of other input variables. For the independent linear normal model, or indeed for any model for which Xi has linear regression on Z, the above measure equals σxiρ(Z,Xi)/σz. When linear regression does not hold, the new sensitivity measures can be compared with the correlation coefficients to indicate degree of departure from linearity. We say that Z is probabilistically dissonant in Xi at Z = z if Z is increasing (decreasing) in Xi at z, but probabilistically decreasing (increasing) at z. Probabilistic dissonance is rather common in complicated models. The new measures are able to pick up this probabilistic dissonance. These notions are illustrated with data from an ongoing uncertainty analysis of dike ring reliability.