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For statistical questions involving the Jacobian matrix (or determinant) of first partial derivatives. For purely mathematical questions about the Jacobian it is better to ask at math SE https://math.stackexchange.com/.
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Polar Coordinate Variable Transformations
I have seen people write $R^{2}=X^{2}+Y^{2}$ and $\theta=\arctan(x/y)$ and blindly finding the jacobian without giving regard to the fact that $tan(\theta)=x/y$ has multiple inverses on $\theta \in (0,2 …