[ENH] numpy and outer product functionality for distribution methods

[fkiraly]

Design issue related to adding outer product evaluation mode to distribution methods.

Related to comments of @FelixWick in #327 (comment).

Currently, BaseDistribution descendants support up-broadcasting of arguments, but not up-broadcasting of results, if arguments with additional dimensions are given. Mathematically, this is related to taking outer products instead of element-wise products, in scalar or vector cases

This is a natural feature to offer, for instance tensorflow.probability functions in this way, and cyclic-boosting also has the feature.

There are a few obstacles for adding this:

• expectations on public inputs and outputs being pd.DataFrame
• numpy.ndarray-s - where are not a supported input type
• unclear target interface, e.g., cyclic-boosting has an extra argument that controls elementwise vs outer product, which I find cumbersome and somewhat unintuitive.

Imo the most elegant way to allow this is as follows:

• allow numpy.ndarray and coercibles as input to all distribution methods. These must have shape of the distribution or 1, for dimensions present in the distribution. Inputs that are currently valid - up to 2D coercibles for array distributions, and flots for scalar distributions - are not coerced and treated as presently.
• If a numpy.ndarray is passed, dimensions that are not present in the distribution will lead to output upcasting, special case is outer product mode for scalar distributions.

Examples:

• For a scalar distribution n = Normal(0, 1), passing n.pdf([1, 2, 3, 4, 5]) will lead to evaluation at 5 points, and return a np.ndarray of shape (5,).
• For an array distribution n = Normal([[0, 1], [2, 3]], 1), calling n.pdf([[[1, 2, 3, 4, 5]]]) leads to a return np.ndarray of shape (2, 2, 3) - upcasting happens along the 3rd dimension of length 5 that the argument introduces.

Thoughts, @setoguchi-naoki, @FelixWick, @VascoSch92, @ShreeshaM07 ?

[VascoSch92]

Makes sense to me.