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
 
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