extend model arg usage in io_pymc3 to fix plot_ppc with prior

[OriolAbril]

Description

Try to improve handling of prior groups and observed data in io_pymc3. Related to #1002. It introduces an important change in behaviour, it proposes to exclude the observed_data group whenever predictions are present. @corriebar @rpgoldman

I also extended tests on io_pymc and improved the helper function check_multiple_attrs.

And finally, how do you feel about deprecating the use of from_pymc3 without model nor trace (or even without model). I was thinking on adding a warning. For now not using a model nor trace will raise a pending deprecation warning as a start. @canyon289 @aloctavodia @ColCarroll

Related to #939.

Checklist

• Does the PR follow official
  PR format?
• Is the new feature properly documented with an example?
• Does the PR include new or updated tests to cover the new feature (using pytest fixture pattern)?
• Is the code style correct (follows pylint and black guidelines)?
• Is the change listed in changelog?

[rpgoldman]

I don't really like leaving out the check that tells the caller why they are not getting observations out of their trace when they expect it. Perhaps replace my error with a UserWarning?
It seems like Arviz tries to get whatever information it can out of a trace, and ignores whatever it can't figure out. This makes it relatively robust, but means that the user doesn't know that they could get more information into the InferenceData by providing a model.

[OriolAbril]

I completely agree, I was just waiting in order to replace it with an informative warning or a deprecation warning.

[rpgoldman]

Per my comment in the code and your question in the MR description -- I agree it would be a good idea to require supply of the model. I think this is particularly important because the user could get an inappropriate model out of the trace.
This may seem far-fetched, but for PyMC3 one actually has to move a trace to a new model in some cases in order to do out of sample predictions.

[OriolAbril]

Only the model argument warning-deprecation is left to do, after that we can merge

[OriolAbril]

I decided to start with the deprecation on no model nor trace (it will be triggered in cases such as only prior or only posterior predictive/predictions). We can make it more strict next release by requiring a model even when the trace is present and eventually remove the _straces trick. In my opinion, PyMC3 users should not mind having to call from_pymc3 within a model context or passing the model as kwarg, it already is the workflow for sample, sample_prior_predictive...

I think it is ready to merge

[rpgoldman]

I agree. If the tests pass again, we should merge. Looks very good!

[OriolAbril]

This allows to make prior predictive checks right away with PyMC3!

with pm.Model():
    # define model
    prior = pm.sample_prior_predictive()
    idata = az.from_pymc3(prior) # has to be either from a model context or
                                 # passing model=model to from_pymc3

az.plot_ppc(idata, group="prior")

I am not really sure about the way to advertise this though, is there a PyMC3 tutorial on prior predictive sampling? @canyon289 @aloctavodia

[AlexAndorra]

This is great -- thanks guys!!
To my knowledge, there is no tutorial dedicated to prior pred checks on PyMC's website. I found:

• The putting notebook, where Colin does some prior checks -- but maybe too complicated a use-case for an introduction.

• I updated the radon NB a few weeks ago, and among other things added prior checks. The new version is not up yet (but it's on master if you wanna check it out), but this could be a good avenue to advertise this new use.

• One NB dedicated to posterior predictive checks. We could extend (and update) it -- this would make a useful educational ressource to point to.

In general, I noticed on the Discourse that people find it hard to understand the concept of prior/posterior pred checks -- or just don't know about them. So I think an intro tutorial would be really useful.