Rename from_pymc3(prior) arg to prior_predictive and add prior arg

Tell us about it

Is it unclear whether prior means prior_predictive, or prior samples from reading docs. https://arviz-devs.github.io/arviz/generated/arviz.from_pymc3.html#arviz.from_pymc3

From tests though it looks like this argument should be prior predictive https://github.com/arviz-devs/arviz/blob/master/arviz/tests/test_data.py#L640

Proposal is to rename prior to prior_predictive and include a method for prior samples to be stored in az.InferenceData

Thoughts on implementation

Rename argument to be specific like pystans method https://arviz-devs.github.io/arviz/generated/arviz.from_pystan.html#arviz.from_pystan

@ColCarroll @aloctavodia Let me know what you think and I can go ahead and do this

[rpgoldman]

The thing my PR fixes is that you can’t determine what is constant and what is not based on the trace that sample_prior_predictive returns (or really, the return of any PyMC3 sampling function). The reason is that PyMC3 allows the user to control what variables do and do not appear in the traces that the sampler returns. That is why, as far as I can tell, we must give from_pymc3 the PyMC3 model as an argument: without access to the model, the translator simply doesn’t have enough information to allocate variables to groups. Note also that using the backdoor from the posterior trace doesn’t generally work, either, since if you are doing predictions out of sample, you must create a new PyMC3 model and use the old trace with the new model – meaning that the model cached in the posterior trace is the wrong model.

That was kind of my designer’s notes for the Pull Request!

[rpgoldman]

I agree: we can look at the model and the trace(s) and figure out how to allocate the information between the two groups ourselves, instead of asking the users to.