I have a known matrix M (square of dimension D) and a parameter vector v (of length D) which is unknown to me and whose posterior distribution I am trying to estimate. My prior on v is that each of its components is standard normal.
For example, let's say that M looks like this:
[[1, -1, -1]
[1, 0, 2]
[1, 1, -1]]
My observed data is a of the form R * M * v where R is a "reduction" (non-square) matrix that effectively only allows me to observe some of the components of M * v. For example, R might look like this (keeping the first and second components of M * v):
[[1, 0, 0]
[0, 1, 0]]
What's the right way to set up a problem like this in STAN?