> On Nov 26, 2016, at 11:53 PM, Ben Goodrich <
goodri...@gmail.com> wrote:
>
> On Saturday, November 26, 2016 at 10:34:28 PM UTC-5, Michael Betancourt wrote:
> The most natural thing to do is a hierarchical model
> on the latent, unconstrained space. For a correlation
> matrix that reduces to the N(N-1)/2 lower diagonal
> elements of the Cholesky factor. In other words,
> have N(N-1)/2 independent univariate hierarchical
> models then fill in a the lower diagonal elements
> with those values, ones on the diagonal, and then
> construct Omega.
> This would be easier if the transformation from
>
> real numbers -> canonical partial correlations -> Cholesky factors -> correlation matrices
>
> were exposed in the Stan language.
Absolutely. That's been on the to-do list for a while. This one wouldn't
even need us to expose the Jacobian calculation.
> You could look at the implementations (yes, there are two for reasons I don't understand) in Stan or you could access them yourself with a little C++ in version 2.13.
If you're talking about two functions to do the constraining
transforms, it's because one computes Jacobians and one doesn't.
If it's deeper than that, it may just be a missed opportunity
to consolidate code.
> But perhaps a more fundamental issue is that I don't think anyone knows what hierarchical prior to put on the real numbers in the unconstrained space.
:-) I was just about to ask about that.
- Bob