Standard MvNormal, Inconsistency with Normal, and I

[jessebett]

MvNormal is inconsistent with the syntax for Normal

Constructing a standard univariate Normal is achieved by Normal()
However, MvNormal() is not defined.
I understand this is ambiguous in dimensionality. However it isn't ambiguous to do something like evaluate the pdf of a d-dimensional vector under an MvNormal, as it will necessarily be d dimensional. I wonder if there is a way to have the standard normal defined without dimension stated, for evaluating densities, but sampling from this will obviously not be defined.

When Normal dispatches on a single argument it corresponds to the mean, but when MvNormal dispatches on a single argument it corresponds to the diagonal vector of its sigma... this is pretty strange.
An extreme example is Normal(1.) is a gaussian with mu=1 and sig=1, but MvNormal([1.]) is a 1D gaussian with mu=0 and sig=0...

MvNormal has not been updated to take I for the identity.
The documentation needs to change as well, as it refers to eye(d).

The current way to define a standard d-dimensional multivariate normal isn't great MvNormal(zeros(d),Matrix(I,d,d))

I would like MvNormal(d=3) to produce a 3-dimensional standard multivariate normal.
MvNormal(zeros(3),I) should work as well.

[AzamatB]

The current way to define a standard d-dimensional multivariate normal isn't great MvNormal(zeros(d),Matrix(I,d,d))

With #30298 merged, this can be called as MvNormal(zeros(d),I(d)), but I agree with the rest

[matbesancon]

@jessebett PR very welcome on this

[andreasnoack]

Let's continue this conversation in #826