Arviz: `from_cmdstanpy` doesn't capture log_likelihood when provided as a dict

[jburos]

Describe the bug

When using from_cmdstanpy(CmdStanMCMC, log_likelihood = {'output_name': 'log_lik_parameter_name'}), the log_likelihood group isn't returned in the az.InferenceData object.

However, if I use from_cmdstanpy(CmdStanMCMC, log_likelihood = ['log_lik_parameter_name']), the log_likelihood group is created correctly.

In both cases the log_likelihood is correctly filtered out from the posterior draws, per these lines. However, the log_likelihood_to_xarray method does not address the scenario where the user provides the log_likelihood as a dict (per these lines).

To Reproduce

I updated a gist here to create a CmdStan fit for the same eight_schools model in the documentation.

The gist creates az.InferenceData objects in two ways:

idata_from_cmdstanpy = az.from_cmdstanpy(fit_from_cmdstanpy, dims=dims, coords=coords, log_likelihood = ['log_lik'])
idata2_from_cmdstanpy = az.from_cmdstanpy(fit_from_cmdstanpy, dims=dims, coords=coords, log_likelihood = {'y': 'log_lik'})

Output:

In [2]: idata_from_cmdstanpy
Out[2]: 
Inference data with groups:
        > posterior
        > log_likelihood
        > sample_stats

In [3]: idata2_from_cmdstanpy
Out[3]: 
Inference data with groups:
        > posterior
        > sample_stats

Expected behavior

Both methods of describing log_likelihood output should be supported

Additional context

In [4]: az.__version__
Out[4]: '0.10.0'

[ahartikainen]

log_likelihood accepts str or a list of str. (See docstring)

What would be the purpose of that dict?

[jburos]

Ah, interesting. I was looking at this pystan schema example in the User Guide:

idata_stan = az.from_pystan(
    posterior=posterior,
    prior=prior,
    posterior_predictive=["slack_comments_hat","github_commits_hat"],
    prior_predictive=["slack_comments_hat","github_commits_hat"],
    observed_data=["slack_comments","github_commits"],
    constant_data=["time_since_joined"],
    log_likelihood={
        "slack_comments": "log_likelihood_slack_comments",
        "github_commits": "log_likelihood_github_commits"
    },
    predictions=["slack_comments_pred", "github_commits_pred"],
    predictions_constant_data=["time_since_joined_pred"],
    coords={"developer": names, "candidate developer" : candidate_devs},
    dims={
        "slack_comments": ["developer"],
        "github_commits" : ["developer"],
        "slack_comments_hat": ["developer"],
        "github_commits_hat": ["developer"],
        "time_since_joined": ["developer"],
        "slack_comments_pred" : ["candidate developer"],
        "github_commits_pred" : ["candidate developer"],
        "time_since_joined_pred" : ["candidate developer"],
    }
)

Which includes a dict for the scenario where there are multiple observed values, each with a different log_likelihood.

[ahartikainen]

Ok, yeah. There could an option to rename values.