Further explanation when Potentials have impact on posterior sampling

[williambdean]

When does the use of Potential have an impact on posterior predictive sampling?

pymc/pymc/model/core.py

Lines 2274 to 2278 in 6ef135b

	Warnings
	--------
	Potential terms only influence probability-based sampling, such as ``pm.sample``, but not forward sampling like
	``pm.sample_prior_predictive`` or ``pm.sample_posterior_predictive``. A warning is raised when doing forward
	sampling with models containing Potential terms.

It seems like sampling distributions only given InferenceData.posterior samples would not be affected by Potentials. Is it possible to refrain from warning given
the variables being sampled?

[ricardoV94]

It seems like sampling distributions only given InferenceData.posterior samples would not be affected by Potentials.

What does this mean?

I guess Potentials can only affect what is in their graph, so we could do a fancier check. However, if you have a model with Potentials and know it's safe you can also suppress the warning on your end? We can define a warning subclass to make it easier to filter.

[williambdean]

For instance, examples that use the potential to add a constraint to the parameters of the model. However, this is still a likelihood of the model

pymc/pymc/model/core.py

Lines 2344 to 2353 in af81955

	.. code:: python
	import pymc as pm
	with pm.Model() as model:
	# p(max_items) = 1 / max_items
	max_items = pm.Uniform("max_items", lower=1, upper=100)
	pm.Potential("power_prior", pm.math.log(1/max_items))
	n_items = pm.Uniform("n_items", lower=1, upper=max_items, observed=60)

In comparison, the last example which uses the potential as the primary lielihood of the model

pymc/pymc/model/core.py

Lines 2359 to 2371 in af81955

	.. code:: python
	import pymc as pm
	def normal_logp(value, mu, sigma):
	return -0.5 * ((value - mu) / sigma) ** 2 - pm.math.log(sigma)
	with pm.Model() as model:
	mu = pm.Normal("x")
	sigma = pm.HalfNormal("sigma")
	data = [0.1, 0.5, 0.9]
	llike = pm.Potential("llike", normal_logp(data, mu, sigma))

Is it correct to think the effect of sampling with posterior is different in these two cases? And the first one would not be affected if just looking at the likelihood variable?