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The First Detailed Account of Statistical Analysis That Treats
Models as Approximations The idea of truth plays a role in both
Bayesian and frequentist statistics. The Bayesian concept of
coherence is based on the fact that two different models or
parameter values cannot both be true. Frequentist statistics is
formulated as the problem of estimating the "true but unknown"
parameter value that generated the data. Forgoing any concept of
truth, Data Analysis and Approximate Models: Model Choice,
Location-Scale, Analysis of Variance, Nonparametric Regression and
Image Analysis presents statistical analysis/inference based on
approximate models. Developed by the author, this approach
consistently treats models as approximations to data, not to some
underlying truth. The author develops a concept of approximation
for probability models with applications to: Discrete data Location
scale Analysis of variance (ANOVA) Nonparametric regression, image
analysis, and densities Time series Model choice The book first
highlights problems with concepts such as likelihood and efficiency
and covers the definition of approximation and its consequences. A
chapter on discrete data then presents the total variation metric
as well as the Kullback-Leibler and chi-squared discrepancies as
measures of fit. After focusing on outliers, the book discusses the
location-scale problem, including approximation intervals, and
gives a new treatment of higher-way ANOVA. The next several
chapters describe novel procedures of nonparametric regression
based on approximation. The final chapter assesses a range of
statistical topics, from the likelihood principle to asymptotics
and model choice.
Mathematical Methods for Signal and Image Analysis and
Representation presents the mathematical methodology for generic
image analysis tasks. In the context of this book an image may be
any m-dimensional empirical signal living on an n-dimensional
smooth manifold (typically, but not necessarily, a subset of
spacetime). The existing literature on image methodology is rather
scattered and often limited to either a deterministic or a
statistical point of view. In contrast, this book brings together
these seemingly different points of view in order to stress their
conceptual relations and formal analogies. Furthermore, it does not
focus on specific applications, although some are detailed for the
sake of illustration, but on the methodological frameworks on which
such applications are built, making it an ideal companion for those
seeking a rigorous methodological basis for specific algorithms as
well as for those interested in the fundamental methodology per se.
Covering many topics at the forefront of current research,
including anisotropic diffusion filtering of tensor fields, this
book will be of particular interest to graduate and postgraduate
students and researchers in the fields of computer vision, medical
imaging and visual perception.
Mathematical Methods for Signal and Image Analysis and
Representation presents the mathematical methodology for generic
image analysis tasks. In the context of this book an image may be
any m-dimensional empirical signal living on an n-dimensional
smooth manifold (typically, but not necessarily, a subset of
spacetime). The existing literature on image methodology is rather
scattered and often limited to either a deterministic or a
statistical point of view. In contrast, this book brings together
these seemingly different points of view in order to stress their
conceptual relations and formal analogies. Furthermore, it does not
focus on specific applications, although some are detailed for the
sake of illustration, but on the methodological frameworks on which
such applications are built, making it an ideal companion for those
seeking a rigorous methodological basis for specific algorithms as
well as for those interested in the fundamental methodology per se.
Covering many topics at the forefront of current research,
including anisotropic diffusion filtering of tensor fields, this
book will be of particular interest to graduate and postgraduate
students and researchers in the fields of computer vision, medical
imaging and visual perception.
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