Remove automatic normalization in Multinomial and Categorical

[ricardoV94]

This cropped up in #5234

Should we stop doing automatic normalization of the p parameter? This can hide very wrong inputs such as

import pymc as pm

with pm.Model() as m:
  x = pm.Multinomial('x', n=5, p=[-2, -2, -2, -2])

m.logp({x: [3, 2, 0, 0]})
# array(-4.62888666)

If we decide to keep the automatic normalization, we can at least remove some checks in the logp definition, since they cannot be triggered in this case.

[ericmjl]

I'm in favour of this. Explicit is better than implicit!

[twiecki]

I think this caused some problems e.g. if you a user specifies [.3, .3, .3] where things almost line up.

[fonnesbeck]

Perhaps have a normalization tolerance, where for example [.33, .33, .33] gets normalized but more egregious values raise an exception? Then at least the user has to be explicit about how close they allow themselves to be.

[ricardoV94]

The tolerance can be adjusted with at.isclose check, or we can simply do like the Dirichlet value and not even check if the probabilities add up to one (we can just check if they are in the unit range)

[ricardoV94]

Here is an idea. Whenever the user creates a Multinomial / Categorical distribution with concrete (numpy) values we check if they are valid and if not we normalize them but also issue a UserWarning along the lines of:

p values sum up to 0.9, instead of 1.0. They will be automatically rescaled. You can rescale them directly to get rid of this warning.

In the logp or whenever we have symbolic inputs we don't do any invisible normalization, and let it evaluate to -inf as with invalid parameters in other distributions.

I think this covers most of the user cases and does not have big backwards compat issues.

[twiecki]

I like that.

[ericmjl]

Same here!