cholesky_factor_corr

[Vishv Jeet]

Is there a way to constrain parameters in cholesky_factor_corr to have only positive values?

regards,

vishy

[Ben Goodrich]

On Friday, January 27, 2017 at 4:20:29 PM UTC-5, Vishv Jeet wrote:

Is there a way to constrain parameters in cholesky_factor_corr to have only positive values?

No. You probably want a kernel function for that.

Ben

[Bob Carpenter]

Do you want the correlations to be positive or the
cholesky factor to be only positive? The latter can
be done with transforms and a Jacobian following the
way we do the Cholesky factor itself. The former would
be easy for a 2 x 2 correlation matrix, but I don't know
how to do it for anything larger.

- Bob

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[Vishv Jeet]

Thank you. I want the correlations to be all positive, I did'nt realize that keeping cholesky factor positive is an overkill. I will work out the Jacobian.

Do you want the correlations to be positive or the
cholesky factor to be only positive? 

[Ben Goodrich]

On Saturday, January 28, 2017 at 7:55:19 AM UTC-5, Vishv Jeet wrote:

Thank you. I want the correlations to be all positive, I did'nt realize that keeping cholesky factor positive is an overkill. I will work out the Jacobian.

Yes, this is the difficulty. There are correlation matrices with all positive correlations for which the lower-triangular elements of the Cholesky factor have mixed signs. And Cholesky factors with all positive lower-triangular elements when multiplied together only cover a subset of the correlation matrices with all positive correlations.

Ben

[Michael Betancourt]

A Gaussian with positive correlations is exchangeable, and

as the dimensions increase it will asymptote to a hierarchical

model.  So you probably just want to just build a hierarchical 

model explicitly.