Tag: spherical

Proof: If the marginal distribution is Gaussian, the joint distribution is clearly spherical. Below we show the converse: if the joint distribution is spherical, the marginal distribution is Gaussian. Let the marginal distribution be $g(x)$, so $p(x,y) = g(x)g(y)$. Spherical means the gradient of the joint distribution is proportional to $(x,y)$. That is $$\nabla p(x,y)…