On the dynare wiki page, it says that when there is a one-to-one relationship between the coefficients (\textbf{A}) of the VAR model and the parameters of the DSGE model plus the prior weight (\theta, \lambda), it will be a good idea to estimate (\theta, \lambda) instead of \textbf{A}.

But does a one-to-one relationship between \textbf{A} and (\theta, \lambda) occur very often in DSGE-VAR models? In my mind that would be kinda hard to achieve. Or maybe I am not conceptualizing it well?

And when we do not have a one-to-one relationship between \textbf{A} and (\theta, \lambda), \theta and \lambda must still be known, right? To be able to get the prior p_0(A, \Sigma \;| \theta, \lambda).