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