I am facing an inverse problem with two input variables and two

output variables. I think it is well posed problem.

I am looking for STAN modeling example to attack this problem

instead of using so-called Newton algorithm.

Do you know about a package appropriate for this purpose?

Concerning the conjugacies of prior distribution and posterior distribution

By using conjugation, I think one can derive an approximate solution of the inverse problem.

Do you know about an example to analytically solve

this based on Bayesian statistics?

Thx in advance,