Request for vector return from normal_cdf given vector arguments

[adkinsty]

I wish to execute the normal CDF on vector inputs to obtain a vector of cumulative probabilities. However, I am getting a dimension mismatch error. The error says the return on the right-hand side is of type “real”. The Stan documentation says that the cdf function accepts “reals” arguments and has “reals” returns. I thought this psuedotype “reals” included vectors yet it appears to be returning a scalar.

Example code:

vector[N] mu;
vector[N] sigma;
vector[N] x;
vector[N] phi;

phi = normal_cdf(x, mu, sigma);

Example error:

SYNTAX ERROR, MESSAGE(S) FROM PARSER:
Dimension mismatch in assignment; variable name = phi, type = vector; right-hand side type = real.
Illegal statement beginning with non-void expression parsed as
  phi

[SteveBronder]

Yes all the lpdf and cdf functions return back a scalar. A real in the stan language is a scalar

It would be nice to have a vlpdf style function that returned a vector but we haven't had time to implement it

[spinkney]

This would be nice to have for all the copula stuff as well. As the copulas use the marginal cdfs evaluated at each data point.

[wds15]

But I think there would not really be a performance gain..so these functions can live in Stan language is what I would think.

[spinkney]

But I think there would not really be a performance gain..so these functions can live in Stan language is what I would think.

+1 ^

also, the row/col-wise framework proposed by @andrjohns would solve this issue.

[wlandau]

This feature would really help when we need access to individual observation-level log likelihoods but still want to take advantage of the vectorization in the _lpdf functions. Example: https://arxiv.org/abs/2209.09190

[hansvancalster]

It would also help in case of interval censoring. See this comment: https://github.com/paul-buerkner/brms/issues/1657#issuecomment-2367156113

[SteveBronder]

I have a PR that examples how we can do this. The main thing is it's a huge rewrite of our distributions that would be a lot of elbow grease effort. It would be nice to have a Stan hackathon to go through the distributions with people and do this split up over several people. We also need a test suite change so that all these are tested for vector returns

https://github.com/stan-dev/math/pull/2751