Implementation

The primary concern in implementing PDF projection is the calculation of the J-function (2.3). The numerator density $p({\bf x}\vert H_0)$ is generally some canonical distribution, such as Gaussian or Exponential. Sometimes, if using a floating reference hypothesis (See Section 2.3.3), $p({\bf x}\vert H_0)$ must be carefully designed. But it is the denominator density $p({\bf z}\vert H_0)$ that presents the biggest challenge. Below, we discuss a variety of methods to obtain the J-function.