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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
Mathematical and Statistical Aspects of Inverse Problems 63
for θ , i.e., solving (3.38). However, we note the GLS relations hip (3.38) does
not follow fr om minimizing the weighted least squares with weights chosen as
w
j
= f
2γ
(t
j
; θ) (see p. 89 of [35]).
Another motivation for the GLS estimating equations (3.37) and (3.38) can
be found in [18]. In that text, Carroll and Ruppert claim that if the data are
distributed according to the gamma distribution, then the maximum-likelihood
estimate for θ (a standard approach when one assumes that the distribution
for the measurement error is co mpletely known—to be discussed later) is the
solution to
N
X
j=1
f
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Publisher Resources

ISBN: 9781482206432