Sensitivity to correlation in multivariate models - Žanić, Vedran; Žiha, Kalman (Computer Assisted Methods in Engineering and Science, 2023)
The paper presents some aspects of the sensitivity analysis within the multivariate distribution models. The presented procedures are provided for engineering problems based on the Nataf model. The Nataf model involves the marginal distributions of the random variables and the correlation between them. Sensitivities are considered through derivatives with respect to the correlation coefficients. The terms for the derivatives of the Nataf correlation coefficients with respect to the given correlation coefficients are presented. The derivatives of the transformations between the random variables are given next. The Cholesky decomposition and the spectral decomposition are applied. Derivatives of the Cholesky decomposition are obtained in the form of a recursive scheme. Derivatives of the eigenvalues and eigenvectors are obtained using perturbations. In addition, a comprehensive method for derivatives of distances and derivatives of angles between the directions is given. Finally, numerical examples are attached to illustrate the presented procedures.