vector-output log density functions

[bob-carpenter]

Idea from Aki Vehtari on stan-dev:

In Stan 2.8, log density functions like normal_log() output the sum of the densities of their components (with appropriate broadcasting of scalars).

It would be nice to allow them to be specified to return a vector, for instance for WAIC or LOO calculations. Aki suggests somethign roughly like

log_lik <- normal_ld<norm=true, sum=false>(y | X * b, sigma);

or maybe with vec=true instead of sum=false.

The result of #1683 will help with implementation.

[danielinteractive]

Just found this, this would be really useful in many situations.

[bob-carpenter]

+1. There have been more and more cases where I've wanted to do this. It shouldn't be too hard by decorating the log density functions with one more layer of suffix.

[SteveBronder]

Yes I think it's very doable as laid out above, mostly need to find time do it. There's a few places we need to be careful but for the most part a couple template tricks should handle everything

[WardBrian]

For me I think my question is whether the <> syntax is the right choice for this? The alternative that comes to my mind is if we add a keyword argument syntax