Biomedical Engineering Reference
In-Depth Information
where Q
k
= ( Q
k
; Q
k
) and g
k
= ( Q
k+1
; Q
k+1
), and set L
m+2
(Q
m+2
) =
L
m+2;0
( Q
0
m+2
) + L
m+2;1
( Q
1
m+2
), with Q
m+2
= ( Q
0
m+2
; Q
1
m+2
). In addition,
the log-likelihood loss, defined as L
V
(Q
V
) = log Q
V
, will be used for com-
ponent Q
V
of Q. For each k 2f0; 1;:::;m + 2g, given component
Q
k
, we may
define the fluctuation
!
h
1
(a;v)
Q
k1
r=0
g
r
(a)(o)
Q
k
(
k;a
)(o) = expit
Q
k
(o) +
k
logit
and corresponding fluctuation sub-model Q
k
( Q
k
) = f Q
k
(
k;a
) : j
k;a
j < 1g,
where we have dened
h
1
(a;v) = h(a;v) (z
1
(a;v);z
2
(a;v);:::;z
R
(a;v)) :
In this set of fluctuation sub-models, the fluctuation parameter
k
is common
to both Q
k
( Q
k
) and Q
k
( Q
k
); a typical member of the joint fluctuation sub-
model will be denoted by Q
k
(
k
) = ( Q
k
(
k
); Q
k
(
k
)). Any fluctuation sub-
model for Q
V
with parameter
V
and score
X
h
1
(a;V )
Q
0
(V ) m
(Q)
(a;V )
D
V
(O) =
a2f0;1g
at
V
= 0 can be selected. We can verify then that, for k 2f0; 1;:::;m + 1g,
d
d
k
L
k
(Q
k
(
k
); g
k
) = D
k
;
where we have that
X
Q
k+1
Q
k
:
I( A(k 1) = a
0;a
(k 1))
h
1
(a;V )
D
k
(O) =
Q
k1
r=0
g
r
(a)
a2f0;1g
With D
m+2
defined similarly, we also find that
d
d
m+2
L
m+2
(Q
m+2
(
m+2
)) = D
m+2
:
The ecient influence curve D
of can be shown to be
"
@
@
E (D
)
#
1
=(P
0
)
D
=
D
Search WWH ::
Custom Search