The goal is to approximate some unknown distribution,
denoted by
or just by
,
by converting
into a PDF of .
We call this PDF projection
since the PDF
is *projected* onto the
input data space. So, given that we know
(or have estimated)
, what does this tell us about
? Let
be the set
of PDFs which *generate*
through
. More precisely, if
then samples drawn from PDF
, and passed through
must
have PDF
. We denote PDFs that
are members of
by
.
Thus, PDF projection is a matter of finding
a member of
.
The reference hypothesis appears in the
argument list because each member distribution of
is uniquely determined by [5].
The entirety of all PDFs in
are found by selection of .

Baggenstoss
2017-05-19