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Modeling and Inverse Problems in the Presence of Uncertainty (Paperback)
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Modeling and Inverse Problems in the Presence of Uncertainty (Paperback)
Series: Chapman & Hall/CRC Monographs and Research Notes in Mathematics
Expected to ship within 12 - 17 working days
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Modeling and Inverse Problems in the Presence of Uncertainty
collects recent research-including the authors' own substantial
projects-on uncertainty propagation and quantification. It covers
two sources of uncertainty: where uncertainty is present primarily
due to measurement errors and where uncertainty is present due to
the modeling formulation itself. After a useful review of relevant
probability and statistical concepts, the book summarizes
mathematical and statistical aspects of inverse problem
methodology, including ordinary, weighted, and generalized
least-squares formulations. It then discusses asymptotic theories,
bootstrapping, and issues related to the evaluation of correctness
of assumed form of statistical models. The authors go on to present
methods for evaluating and comparing the validity of
appropriateness of a collection of models for describing a given
data set, including statistically based model selection and
comparison techniques. They also explore recent results on the
estimation of probability distributions when they are embedded in
complex mathematical models and only aggregate (not individual)
data are available. In addition, they briefly discuss the optimal
design of experiments in support of inverse problems for given
models. The book concludes with a focus on uncertainty in model
formulation itself, covering the general relationship of
differential equations driven by white noise and the ones driven by
colored noise in terms of their resulting probability density
functions. It also deals with questions related to the
appropriateness of discrete versus continuum models in transitions
from small to large numbers of individuals. With many examples
throughout addressing problems in physics, biology, and other
areas, this book is intended for applied mathematicians interested
in deterministic and/or stochastic models and their interactions.
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