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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
82 Statistical Computing in Nuclear Imaging
Conditioned on the number of decays (y Y
c
a
nd c d
1
)
p(y|d) =
I
Y
i=1
c
i
!
(ǫ
i
)
c
i
K
Y
k=1
(α
ki
)
y
ki
y
ki
!
!
d
i
!
c
i
!(d
i
c
i
)!
(ǫ
i
)
c
i
(1 ǫ
i
)
d
i
c
i
=
=
I
Y
i=1
p (y
i
|d
i
) =
I
Y
i=1
p(y
i
|c
i
)p(c
i
|d
i
) = p(y|c)p(c|d) (3.25)
1
c d i : c
i
d
i
.
Conditioned on the number of radioactive nuclei (y Y
c
and c r
1
)
p(y|r) =
I
Y
i=1
c
i
!
(ǫ
i
)
c
i
K
Y
k=1
(α
ki
)
y
ki
y
ki
!
!
r
i
!
c
i
!(r
i
c
i
)!
(ǫ
i
q)
c
i
(1 ǫ
i
q)
r
i
c
i
=
=
I
Y
i=1
p(y
i
|r
i
) =
I
Y
i=1
p(y
i
|c
i
)p(c
i
|r
i
) = p(y|c)p(c|r) (3.26)
1
c r i : c
i
r
i
.
If the conditions given in the parentheses in headers of each conditional
Equations (3.24)–(3 .26) are not met, the distributions ar e zero. The above
equations are the basic ...
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Publisher Resources

ISBN: 9781439849347