[proposal] support for IC with multiple variables

[OriolAbril]

Description

Given the number of possibilities and the even larger number of things that can go wrong, I propose to add only a var_name argument (or name/log_likelihood to avoid confusion with var_names that can be a list) and force users to manually add the combined log likelihood data on which they want to calculate loo/waic to log_likelihood group.

We could add some var_names arg instead and a combine arg to sum or concat or maybe even try to cover groupby too, but this will always be more limited that creating the new variable and it will also be more obscure (i.e. two variables with the default coord names var1_dim_0 and var2_dim_0 will be broadcasted to a 2d array when added because their coord names are different, if the user has to manually create the dataarray of pointwise log likelihood, this can be seen before passing it to loo/waic). I find that both xarray and loo/waic are quite obscure and commonly misunderstood subjects to support this choice. The overhead to users I anticipate is checking examples to copy the combine code most similar to their situation which I actually see like an advantage as it will force them to think about which of the examples better fits their particular case.

closes (maybe) #998 and #987. By maybe I mean that everything will be possible but we will still be missing detailed examples and guidance on how to do it.

Checklist

• Follows official PR format
• New features are properly documented (with an example if appropriate)?
• Includes new or updated tests to cover the new feature
• Code style correct (follows pylint and black guidelines)
• Changes are listed in changelog

[codecov]

Codecov Report

Merging #1173 into master will increase coverage by 0.18%.
The diff coverage is 100.00%.

@@            Coverage Diff             @@
##           master    #1173      +/-   ##
==========================================
+ Coverage   93.05%   93.23%   +0.18%     
==========================================
  Files          94       94              
  Lines        9376     9376              
==========================================
+ Hits         8725     8742      +17     
+ Misses        651      634      -17     

Impacted Files	Coverage Δ
arviz/rcparams.py	93.10% <ø> (ø)
arviz/stats/stats_utils.py	95.66% <ø> (+3.94%)	⬆️
arviz/stats/stats.py	96.20% <100.00%> (+0.35%)	⬆️
arviz/data/io_dict.py	92.92% <0.00%> (+3.03%)	⬆️

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[canyon289]

At a high level I think making things more explicit is good. That being said this is at a depth of diagnostics I dont quite understand. I'll check out this branch locally and give it a try

[OriolAbril]

I think this is ready to merge, it would be great to include in the upcoming release

[aloctavodia]

LGTM. Totally agree on giving user the responsibility. This can be merged once the changelog is updated. We should definitely add a few examples, but that can be done in another PR.

[AlexAndorra]

LGTM, thanks Oriol! I only saw one tiny typo. I'll let it up to you if you want to fix it here or in another PR of yours.

[canyon289]

Looks great. Merging