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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
Model Selection Criteria 147
that the statistical model
Y
j
= f (t
j
; q
0
) + E
j
, j = 1 , 2, . . . , N (4.45 )
correctly describes the observation process. In other words, (4.45) is the true
model, and q
0
is the true value of the mathematical model parameter q.
With our assumption on mea surement errors, the mathematical model pa-
rameter q can be estimated by using the ordinary least squares method; that
is, the ordinary least squa res estimator of q is obtained by solving
q
N
OLS
= arg min
q
q
J
N
OLS
(q; Y).
Here Y = (Y
1
, Y
2
, . . . , Y
N
)
T
, and the cost function J
N
OLS
is defined as
J
N
OLS
(q; Y) =
1
N
N
X
k=1
(Y
k
f(t
k
; q))
2
.
The corres ponding realization
ˆ
q
N
OLS
of q
N
OLS
is ...
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Publisher Resources

ISBN: 9781482206432