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Statistical Computing in Nuclear Imaging
book

Statistical Computing in Nuclear Imaging

by Arkadiusz Sitek
December 2014
Intermediate to advanced content levelIntermediate to advanced
275 pages
9h 12m
English
CRC Press
Content preview from Statistical Computing in Nuclear Imaging
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,cr
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
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Publisher Resources

ISBN: 9781439849347