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Modeling and Inverse Problems in the Presence of Uncertainty
book

Modeling and Inverse Problems in the Presence of Uncertainty

by H. T. Banks, Shuhua Hu, W. Clayton Thompson
April 2014
Intermediate to advanced content levelIntermediate to advanced
405 pages
13h
English
Chapman and Hall/CRC
Content preview from Modeling and Inverse Problems in the Presence of Uncertainty
200 Modeling and Inverse Problems in the Presence of Uncertainty
Thus taking K different sampling maps in
C
, represented by the 1 × n-
dimensional matrices C
k
, k = 1, 2 , . . . , K, we construct the discrete distr ibu-
tion on
K
C
=
K
O
i=1
C
(the k-fold cro ss products of
C
)
P
S
=
K
X
k=1
C
k
, (6.11)
where
a
represents the Dirac measur e with atom at a. Using P
S
in (6.10),
we obtain the GFIM for multiple discrete observation methods taken contin-
uously over [t
0
, t
f
] given by
F (P
1
, P
S
, θ
0
) =
Z
t
f
t
0
K
X
k=1
1
σ
2
(t, C
k
)
T
θ
(C
k
x(t; θ
0
))
θ
(C
k
x(t; θ
0
)) dP
1
(t)
=
Z
t
f
t
0
K
X
k=1
1
σ
2
(t, C
k
)
T
θ
x(t; θ
0
)C
T
k
C
k
θ
x(t; θ
0
)dP
1
(t)
=
Z
t
f
t
0
K
X
k=1
T
θ
x(t; θ
0
)C
T
k
1
σ
2
(t, C
k
)
C
k
θ
x(t; θ
0
)dP
1
(t)
=
Z
t
f
t
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Publisher Resources

ISBN: 9781482206432