Use dict_to_dataset_drop_incompatible_coords everywhere

[ricardoV94]

Closes #7891

The example in that issue:

import pymc as pm

with pm.Model(coords={'dim_1': ['a', 'b', 'c'], 'other': [1, 2, 3, 4]}) as m:
    x = pm.Normal('x', mu=0, sigma=1, dims=['dim_1'])
    mu = pm.Deterministic('mu', 1 + x, dims=['other'])
    sigma = pm.HalfNormal('sigma', 1)

    y = pm.Normal('y', mu=mu, sigma=sigma, dims=['dim_1'])
    idata = pm.sample()
    

Outputs

UserWarning: Incompatible coordinate length of 4 for dimension 'other' of variable 'mu'.
The original coordinates for this dim will not be included in the returned dataset for any of the variables. Instead they will default to `np.arange`, possibly right-padded with nan.
To make this warning into an error set `pymc.backends.arviz.RAISE_ON_INCOMPATIBLE_COORD_LENGTHS` to `True`

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📚 Documentation preview 📚: https://pymc--7908.org.readthedocs.build/en/7908/

[ricardoV94]

Some tests failing, meaning the plumbing needs to be tweaked. Anybody interested feel free to take over

[jessegrabowski]

@SelimSBE if you wanted to work on this you can get the tests passing in this PR

[SelimSBE]

@SelimSBE if you wanted to work on this you can get the tests passing in this PR

Sure thing, working on it

[SelimSBE]

@jessegrabowski Quick question: would it be better to publish the fixes I'm working on as part of this PR, or open a separate one?

[jessegrabowski]

Are you able to just push straight into this PR? If we have permissions set up to allow that it's easiest. Otherwise you will have to fork this PR branch and open a new one.

[SelimSBE]

Are you able to just push straight into this PR? If we have permissions set up to allow that it's easiest. Otherwise you will have to fork this PR branch and open a new one.

@jessegrabowski Hi, I don’t have push access to this PR branch, so I’ll open a new PR with the additional changes.