## J-Function

The PDF can be derived if we first orthogonalize the features. Let which can also be written This is the energy in orthogonal to the columns of . Accordingly, is statistically independent of under . Thus, Also, is chi-squared with degrees of freedom,

where and is the Gaussian distribution with mean and co-variance :

And, since can be obtained from using a linear transformation with Jacobian of determinant 1, we can write The J-function is just For more information see the function software/module_lin_gauss.m.

Baggenstoss 2017-05-19