Using LKJ priors

I have a problem where I want to apply the method referred to as “margin” in Pernot, Pascal, and Fabien Cailliez. “A Critical Review of Statistical Calibration/Prediction Models Handling Data Inconsistency and Model Inadequacy.” AIChE Journal , 2016 to solve for model inadequacy.

For the Cholesky component L of the covariance matrix, Vm, I’m using the LKJCholeskyCov, which seems to work well for a 2x2 matrix Vm. What I quite don’t understand, is that in the implementation of LKJCholeskyCov, there is a determinant of the jacobian of the transformation referred to as ϕ−1. Why is that needed?

Will it bee the same thing to use a separate LK prior on the correlation matrix wich pdf© proportional to |C| ^ (eta -1), whatever needed for the standard deviation vector, and then construct Vm as:

Vm = diag(sd) @ C @ diag(sd)

Probably not? I would appreciate it if someone could explain this.

Thanks,

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No one that can provide some feedback on this?

@aseyboldt