
Statistical computing 189
i i
i
′
i
′
State s State s + 1
y
ki
, c
i
y
ki
′
, c
i
′
y
ki
′
+ 1, c
i
′
+ 1
y
ki
− 1, c
i
− 1
y’s and c’s for other voxels are unchanged between s + 1 and s
FIGURE 6.4 Two subsequent states in the OE algorithm Markov chain if the “move”
is successful. Squares represent voxels.
List of Metropolis-Hastings acceptance ratios
F
lat prior:
x
F 1
=
(c
i
′
+ 1 )ǫ
i
c
i
ǫ
i
′
(6.32)
x
F 2
=
α
ki
′
(c
i
′
+ 1 )ǫ
i
α
ki
c
i
ǫ
i
′
(6.33)
Gamma prior:
x
G1
=
(c
i
′
+ ϑ
i
′
ω
i
′
)(ǫ
i
+ ω
i
)
(c
i
+ ϑ
i
ω
i
− 1 )(ǫ
i
′
+ ω
i
′
)
(6.34)
x
G2
=
α
ki
′
(c
i
′
+ ϑ
i
′
ω
i
′
)(ǫ
i
+ ω
i
)
α
ki
′
(c
i
+ ϑ
i
ω
i
− 1 )(ǫ
i
′
+ ω
i
′
)
(6.35)
Jeffreys prior:
x
J1
=
c
i
′
+
1
2
ǫ
i
c
i
−
1
2
ǫ
i
′
(6.36)
x
J2
=
α
ki
′
c
i
′
+
1
2
ǫ
i
α
ki
c
i
−
1
2
ǫ
i
′
(6.37)
Entropy pri or:
x
E1
=
ǫ
i
ǫ
i
′
c
i
′
+ 1
c
i
1−β
(6.38)