Non-Centered Positive definite logged parmeter

I have a quantity that where the top level is log normally distributed and the lower level qauntities are also postive definite with a lower limit that is non-zero. Is it possible to non-center the top-level in the same fashion as you would a typical Gaussian reparameterization?

A shifted lognormal distribution? This should be as easy as defining another parameter and then on the model step applying the shift on the left hand side.

real<lower = 0, upper = min(y)> shift;
for (n in 1:N)
   y[n] - shift ~ lognormal(mu, sigma);

Perhaps I’m thinking about this strangely. Shifting the log-normal is not difficult, but I’m curious about shifting it in a non-cenetered model. does this make sense?

The non-centering is the shift.

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