Tweak DirichletMultinomial logp and refactor some multivariate logp tests

[ricardoV94]

Couple of tweaks/fixes to the logp /docstrings of Multinomial and DirichletMultinomial

Summary:

1. Remove unnecessary constraints on n and a in DirichletMultinomial, related to discussion in Adds tests and mode for dirichlet multinomial distribution #5225. This also solves a minor issue where the logp was returning a 1D vector for the base case instead of just a scalar.
2. Remove similar old reference about constraints on n and p in the docstrings of the Multinomial
3. Simplify vectorized logp tests for the two distributions as well as the Dirichlet

Also:
4. Remove couple old/redundant random tests

[codecov]

Codecov Report

Merging #5234 (0549f93) into main (a16ec4a) will increase coverage by 0.02%.
The diff coverage is 100.00%.

@@            Coverage Diff             @@
##             main    #5234      +/-   ##
==========================================
+ Coverage   78.95%   78.98%   +0.02%     
==========================================
  Files          88       88              
  Lines       14232    14231       -1     
==========================================
+ Hits        11237    11240       +3     
+ Misses       2995     2991       -4     

Impacted Files	Coverage Δ
pymc/distributions/multivariate.py	72.52% <100.00%> (+0.61%)	⬆️
pymc/parallel_sampling.py	86.33% <0.00%> (-1.00%)	⬇️
pymc/distributions/continuous.py	96.72% <0.00%> (+0.12%)	⬆️

[ricardoV94]

I don't get why we would automatically normalize the vector p in the Multinomial, but I'm happy to revert those changes if they cause too much trouble. It hides the same problems that were raised in this old issue for the Categorical: #2082 (comment)

[AlexAndorra]

Agreed, the implicit normalization is sneaky and can cause issues down the road

[ricardoV94]

If we changed this, it would make sense to also not normalize things in the Categorical by default...

[ricardoV94]

I reverted the changes to the Multinomial normalization, I'll open a discussion on this for the Multinomial and the Categorical. In the meantime this can hopefully be merged.

[AlexAndorra]

But ncan be a vector too, can't it? E.g if the number of trials vary by observation

[ricardoV94]

Yeah n can be a vector or a matrix, anything as long as dimensions broadcast properly. I put the int to indicate the base case, but perhaps the best is to remove any information of shape and only mention the meaning of the parameters?

[AlexAndorra]

Why not int, vector, matrix ? That's more explicit

[ricardoV94]

I don't find that very helpful. Other multivariate distributions use an ambiguous "array" and most univariate distributions say only "int" or "float" even though they also support vectors and tensors of any shape.

[AlexAndorra]

Same remark as for Multinomial

[AlexAndorra]

Wow, those tests are much simpler now 🤩
LGTM @ricardoV94 -- I just had a question about the n parameter. Once that's settled we can merge

[ricardoV94]

@AlexAndorra I added a commit that harmonizes the docstrings of the 3 distributions. The emphasis is on the dtype of each parameter and the special meaning of the last axis of a and p, which determines the number of categories.

I rather not make it explicitly that n can be multidimensional, and let users expect this to work as it does in other distributions. Otherwise I think it creates more confusion to have, p: int, vector, matrix, ..., since these can be of arbitrary dimensionality as long as they broadcast well with a.

[AlexAndorra]

Yeah, that looks better now, thanks @ricardoV94