Hello gurus, I would like to implement a model with a ragged array of simplexes. In response to this query about a year ago, Bob mentions (I think) that there was an intention to expose the simplex_constrain function and log determinant of the Jacobian, which would facilitate this: https://groups.…

[image] jeffeaton: I was wondering if this was implemented? No

Unfortunately this will lead to a non-identified posterior given the over-parameterization. In general this approach works poorly with MCMC.

data { int<lower=2> K; } parameters { simplex[K] pi; vector<lower=0>[K] gamma; } model { target += exponential_lpdf(gamma | 1); } generated quantities { vector[K] pi_rescaled = gamma / sum(gamma); } yields Inference for Stan model: simplexes. 4 chains, each with iter=2000; warmup=1000; t…

I’ve seen it mentioned on the forums, here and other threads, that this kind of non-identifiability can be problematic - but practically it seems to work sometimes, and is even implemented in the unit vector transformation, and is covered in the manual as an example in the “Reparameterizing a Studen…

There’s a quick discussion in the manual. Stan should fail to fit if there’s unbounded non-identifiability in the model. Usually there’s some kind of weak identifiability through priors (including bounds), in which case, your mileage will vary depending on the specifics.

Thanks @bob_carpenter , I guess I’m still confused since it seems like some sections of the manual (23.1 mitigating the invariances) seem to say that non-identifiabilities are bad and should be eliminated, others say that it is fine if it is constrained (unit vector) and others seem to have no issue …

[image] aaronjg: I feel like there is some nuance between these different cases that I am missing… I think you may have misinterpreted my post as being literal.

All well and good if you want to sample directly from a Dirichlet, which is not the relevant task here. When sampling directly there’s no problem because the constraint is applied only after the fact. When using this is a prior, however, you have to confront the non-identifiability. The Gamma pri…

I didn’t realize your relevant tasks required 64 bit integers. With multinomial data that Stan can actually ingest, the phenomenon you are referring to manifests itself in the leapfrogger taking more and smaller steps and yields imprecise estimates of the irrelevant vector gamma, but MCMC sampling f…

In exchange for substantial increases in computation – 2^17 leapfrog steps is a huge computational burden that will make many analyses impractical. I think that’s a pretty fair criterion for “not working well”.

2^17 for over 4 billion observed counts that pin the posterior distribution of pi down to many decimal places. If you only have a couple hundred thousand counts, then you don’t have to change max_treedepth to get the same essentially perfect estimates.

Ragged array of simplexes

Modeling

bgoodri July 26, 2017, 6:57pm 10

I think you may have misinterpreted my post as being literal.

Two parameter distribution over the simplex

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Ragged array of simplexes

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