Should logprob collapes logp terms across dimensions where values interact?

[ricardoV94]

import pymc as pm
x = pm.Normal.dist(shape=(5,))
y = x.cumsum()

pm.logp(y, [1, 2, 3, 4, 5]).eval()
# array([-1.41893853, -1.41893853, -1.41893853, -1.41893853, -1.41893853])

Whereas the equivalent GRW returns a scalar

z = pm.GaussianRandomWalk.dist(shape=(6,), init_dist=pm.DiracDelta.dist(0))
pm.logp(z, [0, 1, 2, 3, 4, 5]).eval()
# array(-7.09469267)

This would simplify some of our uses of the logprob submodule, e.g.:

pymc/pymc/distributions/timeseries.py

Lines 236 to 249 in 1c1695e

	@_logprob.register(RandomWalkRV)
	def random_walk_logp(op, values, init_dist, innovation_dist, steps, **kwargs):
	# Although we can derive the logprob of random walks, it does not collapse
	# what we consider the core dimension of steps. We do it manually here.
	(value,) = values
	# Recreate RV and obtain inner graph
	rv_node = op.make_node(
	reconsider_logprob(init_dist), reconsider_logprob(innovation_dist), steps
	)
	rv = clone_replace(
	op.inner_outputs, replace={u: v for u, v in zip(op.inner_inputs, rv_node.inputs)}
	)[op.default_output]
	# Obtain logp of the inner graph and collapse steps dimension
	return logp(rv, value).sum(axis=-1)

Related discussion in the case of timeseries: #6090 (comment)

This would make sense together with #6360, so that internally we represent a MeasurableCumsum as having ndim_supp +1 from whatever the measurable input was.

On the other hand it could make some cases more difficult to handle. E.g., with Scan we can have some graphs where values are dependent and others where they aren't. This shouldn't be too hard to analyze, but would require extra logic.