 # Ill-posed linear regression

I want to solve the ill-posed problem y = A x, where

“y” is a known vector (1-d) of data,

“A” is a 2-d matrix with parameters theta.

The functional form of A is known, so you can calculate A as function of the parameters. The vector (1-d) “x” are the unknown values that together with the parameters theta are the ones I want to calculate with the bayesian linear regression.

Thus, the question is how can you write this model in Stan

Extra question: because this is an ill-posed problem, do you have to add an extra term such as the one in Tihkonov regularisation?

Is this problem statistical in the sense that y is sampled from Ax with uncertainty, or is this just about finding the set of valid solutions to the strict equality?

Dear Jacob:
This is certainly not just about finding the set of valid solutions to the strict equality.
We obtain y in an independent procedure with uncertainty.
We want to model y ~ Ax + eps, where eps (uncertainty) is modelled by N(0,sigma).