Biomedical Engineering Reference
In-Depth Information
and we have
1
= 0 and
1
= 1. When J > 1, for j = 1,
h
X
i
X
1
=
1
1fa
k
2 [0;
1
)gZ
i
e
ik
+ c
0
'(
2
)=(1 + c
0
);
i
k
1
= c
0
w
2
=(1 + c
0
);
for j = 2;:::;J 1,
h
X
i
X
j
=
j
1fa
k
2 [
j1
;
j
)gZ
i
e
ik
+ '(
j1
)=2 + '(
j+1
)=2;
i
k
j
= w
2
=2;
and for j = J,
h
X
i
+ '(
J1
);
X
J
=
J
1fa
k
2 [
J1
;
J
)gZ
i
e
ik
i
k
J
= w
2
:
It can be shown that (7.14) is log-concave and, hence, '(
j
) can be sampled
via the adaptive rejection algorithm of Gilks and Wild (1992).
7.3.2.2
Birth Move
First, we generate a new jump time
uniformly from G nf
1
;
2
;:::;
J
g.
Suppose
2 (
j1
;
j
). The new J + 1 jump times are relabeled as follows:
jump times before
keep their indices;
becomes the j-th jump time; jump
times after
advance their indices by 1. Denote the new jump times as
j
,
j = 1; 2;:::;J + 1. After the insertion of a new jump time, the two constant
pieces on interval [
j1
;
j
) are sampled as follows:
'(
j
) =
1
'(
j1
) +
2
'(
j
) + u
;
'(
j+1
) =
1
'(
j
) u
+
2
'(
j+1
);
(7.15)
where
1
= (
j
j1
)=(
j+1
j1
),
2
= (
j+1
j
)=(
j+1
j1
), and u
is generated from a uniform distribution U(
0
;
0
) with tuning parameter .
Here u plays the role of an auxiliary variable to the old model and helps to
Search WWH ::
Custom Search