So I posted a while back on my dissatisfaction with the increasing constraint to zero that the multivariate normal imposes in high-dimensional scenarios, and I also posted an alternative that I thought was somewhat promising, if more in the “sufficient stats” spirit than generative. It seemed to wor…

I’ve made a smidge of progress on this. At least, I backed off my attempts at optimization a bit and instead of attempting to use sufficient stats for the correlation structure, I use multi-normal, but (in contrast to the standard approach) do so in a pairwise fashion. This seems to be working decen…

I haven’t really gotten a handle on the code, but is the pairwise formulation in the first post above not missing a Jacobian adjustment on the atanh? Edit: The empirical correlation no longer transformed data, but rather a parameter, right? And actually, the transformation isn’t just the atanh, it…

[image] jsocolar: The empirical correlation no longer transformed data, but rather a parameter, right? And actually, the transformation isn’t just the atanh , it’s the dot product too, which seems like it’ll pose problems… Correct on both accounts.

Also, I’ve just seen OpenCL symmetric eigensolver · Issue #2498 · stan-dev/math · GitHub . If the Stan gets a fast enough eigendecomposition, I wonder how it would behave in practice to implement a prior on the covariance matrix by putting some arbitrary (symmetric) elementwise prior on the elements…

You can already do this in Stan [image] Ensure correlation matrix is positive semi-definite? Modeling You can find a near PSD correlation matrix to the given priors. PSD matrices are really rare compared to all square matrices, especially so as the dimension increases. Y…

@spinkney this is really cool! But I don’t think it accomplishes quite the same thing. I think that your formulation will just cause the model to see the parts of the prior that where valid correlation matrices are least common as being really unlikely a priori, right? Like the prior predictive d…

[image] spinkney: You can already do this in Stan Not sure if you meant “this” to refer to my goals, or something related to @jsocolar ’s ideas; certainly I don’t think it’s pertinent to my goals since the whole point it to get away from the PSD constraint, which so far as I understand is the …

So what @jsocolar says is that he wants a nearest PSD but you’re saying you don’t. From @jsocolar ’s post, I understood his suggestion as finding the nearest PSD. Say you have a sample pairwise covariance matrix as a prior and you want the nearest valid PSD covariance matrix using Stan. You can flat…

[image] spinkney: The covariance matrix will be PSD by construction and then sample pairwise priors will attempt to get your valid PSD covariance close to those elements. Suppose I put uniform priors on the elements of a correlation matrix. Consider what happens in a region of parameter space…

Just FYI, I’m still working on cleaning up my reprex, which I’ll post shortly so you guys can generate the kind of data I’m talking here, but in the interim here’s the inference performance of a standard multivariate normal amid most true correlations=0 and some =.9: [image] So you can see the on…

"Pairwise" alternative to multivariate normal isn't behaving for the hierarchical case; help?

Modeling

spinkney June 9, 2021, 4:46pm 6

You can already do this in Stan

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"Pairwise" alternative to multivariate normal isn't behaving for the hierarchical case; help?

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