Add convenient function to access list of inference methods

[tomicapretto]

In #775 we got access to a great variety of samplers through bayeux. Now I realize it's not that easy to get a list of inference methods. The docstring mentions model.backend.inference_methods['bayeux'] but that means we not only need a Bambi model, but a Bambi model that has already been built.

I think we should have a convenient function to get that list in an easier way. I imagine something like:

import bambi as bmb

bmb.get_inference_methods()

that uses the existing logic to return the appropriate list of inference methods, depending on whether bayeux is installed or not.

[GStechschulte]

The reason we need a defined and built Bambi model is because with bayeux algorithms are dynamically determined at runtime.

I do think it should be simpler to obtain a list of inference methods. I can imagine defining a "dummy model" similar to here to return a list of methods without the user needing to define and build a model.

Another area of improvement I see is how the user can obtain the set of kwargs for a particular inference method. Currently this requires calling bayeux directly, e.g.

bx.Model.from_pymc(model.backend.model).mcmc.blackjax_nuts.get_kwargs()

Since different samplers have different kwargs, it should be easier for the user to know what these are.

[tomicapretto]

I agree the dummy model is the way to go. So what we need is a function similar to the one you linked, that also includes the alternatives built-in pymc, right?

[GStechschulte]

Yup, I believe so. I can work on it this week 😄

[GStechschulte]

We also need to restrict what is returned when calling get_inference_methods. Currently, model.backend.inference_methods returns all bayeux methods. However, Bambi does not implement bayeux optimize algorithms for example.

Nonetheless, if the user attempts to pass jaxopt_bfgs to fit the model, the following error will be raised

NotImplementedError: 'jaxopt_bfgs' method has not been implemented

We should be more consistent to not confuse the users.