Improve support of nested models

[lucianopaz]

At the moment, pymc.Model instances serve two purposes:

1. Book keeping of the different random variables that are created within their context.
2. Namespaces, where each random variable that is created within the context gets the model's name as a prefix to its own name.

The book keeping functionality enables nice features out of the box, like being able to draw the probabilistic graph of only a subset of random variables with graphviz:

with pm.Model(name="m1") as m1:
    a = pm.Normal("a")
    with pm.Model(name="m2") as m2:
        b = pm.Normal("b")
        c = pm.HalfNormal("c")
        d = pm.Normal("d", b, c, shape=10)
    e = pm.Normal("e", a + d, shape=10)
pm.model_to_graphviz(m1)
pm.model_to_graphviz(m2)

renders the following graphs:

The main problem is that the child model does not inherit its parents coords. Note that this snippet leads to an error because m2 does not define the "dim" dimension:

COORDS = {"dim": range(10)}
with pm.Model(name="m1", coords=COORDS) as m1:
    a = pm.Normal("a")
    with pm.Model(name="m2") as m2:
        b = pm.Normal("b")
        c = pm.HalfNormal("c")
        d = pm.Normal("d", b, c, dims="dim")
    e = pm.Normal("e", a + d, dims="dim")

One other problem is that the nested model's name completely supresses the parent model's name. Note that d.name is "m2_d" and not "m1_m2_d", which is more consistent in my opinion.

I've opened this discussion to ask if there's any interest in having nested models inherit their parent's coordinates, and whether their name should also include their parent's name, if any.

The first point is fairly straightforward to implement. We only need to copy the pattern that is used in the free_RVs, etc, attributes as done here and apply it also to the model's _coords, _RV_dims and _dim_lengths attributes.

The point about the model name should be even simpler to implement.

[ricardoV94]

Is there a case not to share dims by default?

[lucianopaz]

I don't think so. I think that the parent model should be made aware of any and all changes to the coords done by a nested model, and the nested models should be able to use the coords that were defined in the parent model. This parent/child sharing essentially means that sibling models would also know of the coords from their siblings.

[ricardoV94]

I agree, I think we can open an issue to fix the coords, and leave the discussion open for the name prefix.

[lucianopaz]

I just opened #5344 that should handle the nested model dims and coords. What should we do about the name prefix? I think the best thing to do would be to always add the parent model name as a prefix for the nested model's name.

[ferrine]

What do you think of / as scope separator?
m1/m2/var

[ricardoV94]

Sounds good. If there are no issues with InferenceData because of the slashes, I like it even more than the underscores

[lucianopaz]

I think that slash is a way better alternative to the underscore

[ferrine]

I was aware about limitations and had plans to improve it

[ferrine]

@ricardoV94 slash does not seem to break anything. PyMC+Xarray+Arviz

[ricardoV94]

Perfect, wanna open a PR for this?

[ferrine]

YES