### The Projected PDF

The formula for PDF projection is

 (2.2)

Note that is a function of only because, although appears on the right hand side, is uniquely determined by through (2.1). We show in the appendix (Section 16.4) that indeed is a PDF (integrates to 1), and is a member of . The term

 (2.3)

is called the J-function" because of the analog with the Jacobian in the change of variables theorem[6]. The projected PDF is therefore decomposed into two terms,

The first depends only on the feature transformation and reference hypothesis and can be exactly determined, so does not need to be learned. The second term is the estimated or given feature distribution.

Baggenstoss 2017-05-19