`SymmetricMatrixvariateNormal` as a separate `RandomVariable`

[marvinpfoertner]

Current State

All variants of a Gaussian random variable share a joint interface.

Problem

However, a Gaussian measure on symmetric matrices behaves fundamentally different from a matrixvariate normal distribution with a SymmetricKronecker covariance. This is the case since support is not the same (only symmetric matrices are sampled from a symmetric matrix-variate distribution).

https://github.com/probabilistic-numerics/probnum/blob/2044c8904a6365394da38d2019545a3954ac8396/src/probnum/randvars/_normal.py#L565

Proposed Solution

• [ ] Implement symmetric matrix-variate normal random variables in a different subclass of RandomVariable.

[mmahsereci]

I would second this. One question: Does this only concern SymmetricMatrixVariateNormal, or do we also support the non-symmetric version? (just curious, not saying we need to support the non-symmetric case as well atm)

[JonathanWenger]

I would second this. One question: Does this only concern SymmetricMatrixVariateNormal, or do we also support the non-symmetric version? (just curious, not saying we need to support the non-symmetric case as well atm)

We currently support non-symmetric matrix-variate normal distributions by passing an appropriate mean (as a matrix or linear operator).