I have the following situation. There is a foundation lying on a two layers soil. The Young’s moduli, E_1 and E_2, of the two soil layers are my random variables. The quantity of interest is the maximal settlement U_Y of the foundation under a given load F. Now say that in the deterministic case using mean values of E_1 and E_2 I calculate (with FE software) a settlement of 1 cm. But at the building site I observe a settlement of 1.5 cm. So I perform a bayesian inversion (I first build a PCE on the FE software, very small LOO error) in order to update my probabilistic input. As a result of the bayesian inversion I get the posterior marginals and the correlation matrix. Since the output U_Y is a function of all inputs that feed my FE software/PCE, U_Y \approx f(E_1,E_2), it is logic that my varibles are correlated in order to “match” the observation of 1.5 cm.
What I don’t understand is if for a forward reliability analysis I should use as probabilistic input the uncorrelated posterior marginals or the correlated posterior marginals as explained in Looking for documentation/example of using UQLab results of Bayesian inference for forward UQ or further Bayesian inference. The point is, in reality E_1 and E_2 have no correlation. There is no physical reason to have a correlation between them.
Thank you in advance for your reply!