Is this even possible? Say I have a pdf $p(x,y\mid\phi)$, and a function $z = f(x,y)$. Is there a way to derive $p(z\mid\phi)$? The usual change of variables rule
$$p(z\mid\phi) = p(x,y\mid\phi) ~\left \lvert \frac{d(x,y)}{dz} \right \rvert$$
doesn't seem to help, as the Jacobian is not square and hence no Jacobian determinant.
