
Counting statistics 87
Let’s now consider computatio n of p(g|r)
which is a probability of obtaining
data g conditione d on the number of radioactive nuclei in voxels described by
r. We proceed similar ly as in the case of the derivation of p(g|c) by defining the
subset Y
r
of complete data Y for which the p(y|r) > 0. Using Equation (3.26)
this subset can be defined as a union o f subsets Y
c
for which p(c|r) > 0 and
c ≤ r. To formalize this using a mathematical equation we define
Y
r
=
[
p(c|r)>0,c≤r
Y
c
. (3.35)
With that in mind starting with identity
p(g|r) =
X
c
p(g|c, r)p(c|r), (3.36)
and because of the conditional independence of g and r for given c ( p(g|c, r