
184 Statistical Computing in Nuclear Imaging
the J effreys prior such invariance under reparametrizatio n and an in
terested
reader should consult the classical works of Jeffreys [49] and Lehmann and
Casella [66].
Since the assumption of f
i
for each voxel implies the Poisson distribution,
the Fisher information for 1D Poisson process is equal to (f
i
)
−1
. It follows
that the Jeffreys prior is the square root of this value and equal to
p
J
(f) ∝
I
Y
i=1
(f
i
)
−
1
2
(6.15)
The proportionality sign is used because the prior is improper and the distri-
bution of the prior cannot be norma lized to 1. Again using Poisson distribution
(Equation (6.11)) and marginalizing f
i
’s ...