@twiecki wrote a great description of non-centering a hierarchical model, both why the sampler sometimes has difficulty exploring the space and what to do about it. Diagnosing Biased Inference with Divergences is also a good description, showing tools for diagnosing divergences, and prescribing non-…

I don’t think this is so much a funnel as a problem with the boundary condition that \sigma^2 < \mu(1-\mu). Even though you have the max sigma, your HalfNormal can still attempt to sample values near 0; and thus near the boundary. Edit: It’s probably not even that. My guess is that the gradient of 1…

Your model is not hierarchical right? That’s what the non centered parametrization is usually needed for. Isn’t your issue simply that sigma can easily get too close to zero? That would indicate you needed a more constrained prior on v, or model sigma directly. Also did you try changing target acc…

To answer your original question though. I am not familiar with a way to parametrize the beta in a non centered way. You can’t simply multiply by the sigma and add a mean because it must be bound between 0 and 1. You can parametrize in terms of a Dirichlet times a concentration, but that is not real…

My understanding is Lucifer’s Funnel is in fact a hierarchical model. At least it is a variation of the McElreath’s Devil’s Funnel, described in a chapter devoted to hierarchical models. [image] (If this is a copyright violation, many apologies. Buy the book. It’s useful, well-written, and funny.…

@chartl that’s quite interesting. Out of curiosity, do you see any advantage in an approach like this compared to just using a logitnormal for controlling both mu and sigma (i.e. discarding the beta distribution altogether)?

Depends on the setting. You can recognize the factor \gamma/(1+\gamma) as just an inflation factor over the expected Binomial variance; and in genetics the parameter \gamma (or sometimes 1-\gamma or sometimes the whole ratio) is known as F_{\mathrm{ST}} and reflects the variability of allele frequen…

Nice one, thanks @chartl - I might try this parameterisation in future

@chartl ’s gamma-sigma parameterization also samples well in my actual model, not just the toy example worked here.

You can thank Sewall Wright for this one, I think. :slight_smile:

When I see him, I will thank him. Hopefully not soon.

Non-centered parameterization of a beta distribution?

Questions

chartl March 18, 2021, 2:46pm 15

While I was searching for something completely unrelated, I came across this old thread about beta parametrization, and it links through to “implicit normalization of gradients”:

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Non-centered parameterization of a beta distribution?

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