Revisiting `eta` parameter in `LKJCholeskyCov`

I have recently stated here that I was still puzzled by the eta parameter in LKJCholeskyCov.

I’ve now put together a notebook to test the effect of eta. The outcome is still somewhat inconclusive:

  • Choosing eta seems voodoo, given that results are unaffected over a broad range of the parameter. I will usually leave it at eta=1.
  • Even leaving eta free does not improve the result, and it seems to be challenging for the sampler.
  • Instead of setting high eta, one could use an uncorrelated estimate (that’s expected).

I thought this is worth sharing for documentation. But did I miss anything?

Could someone again, in plain words, recap what the eta does technically? I got from the previous discussion that it has to do with normalization of the correlation matrix, but what does that mean for practical application?

Thank you!


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