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This book brings together the personal accounts and reflections of
nineteen mathematical model-builders, whose specialty is
probabilistic modelling. The reader may well wonder why, apart from
personal interest, one should commission and edit such a collection
of articles. There are, of course, many reasons, but perhaps the
three most relevant are: (i) a philosophicaJ interest in conceptual
models; this is an interest shared by everyone who has ever puzzled
over the relationship between thought and reality; (ii) a
conviction, not unsupported by empirical evidence, that
probabilistic modelling has an important contribution to make to
scientific research; and finally (iii) a curiosity, historical in
its nature, about the complex interplay between personal events and
the development of a field of mathematical research, namely applied
probability. Let me discuss each of these in turn. Philosophical
Abstraction, the formation of concepts, and the construction of
conceptual models present us with complex philosophical problems
which date back to Democritus, Plato and Aristotle. We have all, at
one time or another, wondered just how we think; are our thoughts,
concepts and models of reality approxim&tions to the truth, or
are they simply functional constructs helping us to master our
environment? Nowhere are these problems more apparent than in
mathematical model ling, where idealized concepts and constructions
replace the imperfect realities for which they stand."
Many electronic and acoustic signals can be modelled as sums of
sinusoids and noise. However, the amplitudes, phases and
frequencies of the sinusoids are often unknown and must be
estimated in order to characterise the periodicity or
near-periodicity of a signal and consequently to identify its
source. This book presents and analyses several practical
techniques used for such estimation. The problem of tracking slow
frequency changes over time of a very noisy sinusoid is also
considered. Rigorous analyses are presented via asymptotic or large
sample theory, together with physical insight. The book focuses on
achieving extremely accurate estimates when the signal to noise
ratio is low but the sample size is large. Each chapter begins with
a detailed overview, and many applications are given. Matlab code
for the estimation techniques is also included. The book will thus
serve as an excellent introduction and reference for researchers
analysing such signals.
Many electronic and acoustic signals can be modeled as sums of sinusoids and noise. However, the amplitudes, phases and frequencies of the sinusoids are often unknown and must be estimated in order to characterize the periodicity or near-periodicity of a signal and consequently to identify its source. Quinn and Hannan present and analyze several practical techniques used for such estimation. The problem of tracking slow frequency changes of a very noisy sinusoid over time is also considered. Rigorous analyses are presented via asymptotic or large sample theory, together with physical insight. The book focuses on achieving extremely accurate estimates when the signal to noise ratio is low but the sample size is large.
Originally published in 1988, this classic text treats the
identification of noisy (multi-input and multi-output) linear
systems, particularly systems in ARMAX and state space form. The
book covers structure theory, including identifiability,
realisation and parameterisation of linear systems; analysis of
topological and geometrical properties of parameter spaces and
parameterisations for estimation and model selection; Gaussian
maximum likelihood estimation of real-valued parameters of linear
systems; model selection; calculation of estimates; and
approximation by rational transfer functions. This edition includes
an extensive new introduction that outlines developments since the
book's original publication, such as subspace identification,
data-driven local coordinates and the results on
post-model-selection estimators. It also provides a section of
errata and an updated bibliography. Researchers and graduate
students studying time series statistics, systems identification,
econometrics and signal processing will find this book useful for
its interweaving of foundational information on structure theory
and statistical analysis of linear systems.
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