Add sample_prior function

[AllenDowney]

Back in 2018, I participated in a discussion of an enhancement of PyMC, adding functions to sample the prior, prior predictive, and posterior predictive distributions.

Here’s the PR: #2983

I suggested an API with four functions:

1. sample_prior
2. sample_prior_predictive
3. sample_posterior (synonym for sample)
4. sample_posterior_predictive (synonym for sample_ppc)

In the end, only sample_prior_predictive and sample_posterior_predictive were added.

Reflecting on that decision, I think there are cases where we want to sample from the prior only and not from the prior predictive. For example, in a model that contains a Potential, the sample from the prior predictive would not reflect the Potential and might be misleading (there’s a warning about that). Also, I have encountered a case where sampling from the prior worked correctly, but sampling from the prior predictive generates an error (sometimes).

As an alternative, you could call sample_prior_predictive and specify var_names, but sample_prior as a wrapper for sample_prior_predictive automates the process of identifying unobserved vars and deterministics (that don't depend on observed vars).

So I am considering adding sample_prior to PyMC. What do we think?

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📚 Documentation preview 📚: https://pymc--7833.org.readthedocs.build/en/7833/

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[ricardoV94]

A clarification on the potential question.

It is not about prior vs prior_predictive. It's about whether you do forward or inverse (aka mcmc) sampling. Potentials only act on the logp so they can't be accounted for by forward sampling.

A Potential can be part of the prior, likelihood or both. The current API doesn't allow disambiguating the meaning and I don't think graph analysis can do it either.

Potentials are a case we warn loudly about but they aren't the only that fails. Other cases include using Flat priors or non-default transforms like Ordered. All these should fail or emit a warning when doing forward sampling, be it through prior, prior_predictive or posterior_predictive.

What could be useful would be to allow using mcmc for prior/prior_predictive for the cases where the forward graph is not compatible. I don't think we can do it for posterior_predictive because we would need one / several good draws for every posterior draw.

I don't love the mangling between "kind of distribution" and method of sampling. A better mental model is that sample uses mcmc sampling (what you obtain is up to you, it could be a prior, a posterior or a posterior_predictive... a prior is someone else's posterior). sample_prior_predictive and sample_posterior_predictive use forward sampling and what you obtain with this is again up to you.

All this is pretty orthogonal to the PR but it was a good excuse for my rant.