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An Invariant Approach to Statistical Analysis of Shapes (Paperback)
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An Invariant Approach to Statistical Analysis of Shapes (Paperback)
Series: Chapman & Hall/CRC Interdisciplinary Statistics
Expected to ship within 10 - 15 working days
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Natural scientists perceive and classify organisms primarily on the
basis of their appearance and structure- their form , defined as
that characteristic remaining invariant after translation,
rotation, and possibly reflection of the object. The quantitative
study of form and form change comprises the field of morphometrics.
For morphometrics to succeed, it needs techniques that not only
satisfy mathematical and statistical rigor but also attend to the
scientific issues. An Invariant Approach to the Statistical
Analysis of Shapes results from a long and fruitful collaboration
between a mathematical statistician and a biologist. Together they
have developed a methodology that addresses the importance of
scientific relevance, biological variability, and invariance of the
statistical and scientific inferences with respect to the arbitrary
choice of the coordinate system. They present the history and
foundations of morphometrics, discuss the various kinds of data
used in the analysis of form, and provide justification for
choosing landmark coordinates as a preferred data type. They
describe the statistical models used to represent intra-population
variability of landmark data and show that arbitrary translation,
rotation, and reflection of the objects introduce infinitely many
nuisance parameters. The most fundamental part of
morphometrics-comparison of forms-receives in-depth treatment, as
does the study of growth and growth patterns, classification,
clustering, and asymmetry. Morphometrics has only recently begun to
consider the invariance principle and its implications for the
study of biological form. With the advantage of dual perspectives,
An Invariant Approach to the Statistical Analysis of Shapes stands
as a unique and important work that brings a decade's worth of
innovative methods, observations, and insights to an audience of
both statisticians and biologists.
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