# Uncertainty ranking: Pearson’s correlation¶

This method deals with analyzing the influence the random vector has on a random variable which is being studied for uncertainty. Here we attempt to measure linear relationships that exist between and the different components .

Pearson’s correlation coefficient , defined in , measures the strength of a linear relation between two random variables and . If we have a sample made up of pairs , , …, , we can obtain an estimation of Pearson’s coefficient. The hierarchical ordering of Pearson’s coefficients is of interest in the case where the relationship between and variables is close to being a linear relation:

To obtain an indication of the role played by each in the dispersion of , the idea is to estimate Pearson’s correlation coefficient for each . One can then order the variables taking absolute values of the correlation coefficients: the higher the value of the greater the impact the variable has on the dispersion of .

(Source code, png, hires.png, pdf)

API:

Examples:

References:

Saltelli, A., Chan, K., Scott, M. (2000). “Sensitivity Analysis”, John Wiley & Sons publishers, Probability and Statistics series

J.C. Helton, F.J. Davis (2003). “Latin Hypercube sampling and the propagation of uncertainty analyses of complex systems”. Reliability Engineering and System Safety 81, p.23-69

J.P.C. Kleijnen, J.C. Helton (1999). “Statistical analyses of scatterplots to identify factors in large-scale simulations, part 1 : review and comparison of techniques”. Reliability Engineering and System Safety 65, p.147-185