Artifacts of sign-fixing in models with sign ambiguity

[aaronjg]

@Bonnevie

I normalize each factor (columns of B) to have unit length

From the model it looks like you are normalizing Sigma to sum to zero, but not B?

If you want B to have unit length, you could compose it from unit_vectors, but then you’d need to make some modifications to keep the sign on the first element positive.

Also, as Ben says about this parameterization of the ordered simplex:

@bgoodri

Opinions differ as to whether this is a disaster or works perfectly fine.
( Ordered Simplex - #2 by bgoodri )

and some more discussion on this sort of thing in this thread:

Ragged array of simplexes

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 be constructed by normalizing a set of unit-scale but independent Gamma random variables: Thus, in Stan you declare a looooong vector of non-negative parameters parameters { vector<lower=0>[sum…

Something to look into, though I’m not sure that is the root cause of the identifiability issue.