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

Many thanks Ben. I did a quick port of the C++ functions to Stan functions, pasted below in case useful for any others. (Not optimally efficient because it duplicates the transform calculation, but works in a pinch.) Thanks, Jeff /** * Return the simplex corresponding to the specified free v…

That is quite possibly correct but more complicated than necessary. Dealing with simplexes of different sizes is annoying, but it it actually the least annoying of the ragged arrays. The trick to avoiding having to deal with Jacobians is to remember that a Dirichlet distribution over simplexes can b…

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…

Ragged array of simplexes

Modeling

bgoodri July 25, 2017, 12:30am 2

Ordered simplex constraint transform

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Ragged array of simplexes

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