An Invariant Approach to Statistical Analysis of Shapes

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9780849303197: An Invariant Approach to Statistical Analysis of Shapes

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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The appearance of this book by Subhash Lele and Joan Richtsmeier is to be welcomed. In recent years there has been much discussion of the relative advantages of morphometric methodology developed by Fred Bookstein and his colleagues versus the EDMA approach advocated by Lele and Richtsmeier. Now readers can decide for themselves.
-Short Book Reviews, Vol. 21, No. 2, August 2001

The invariance principle, a beautiful mathematical concept, is used, alongside statistical techniques, to analyze various biological shapes and forms... Landmark coordinate data technique is used throughout, with topics covered ranging from the study of growth and form to Euclidean distance matrix analysis and applications. In addition to end-of-chapter summaries, useful algorithms, and end-of-text bibliography, various applications are provided of a wide range of problems that transcend disciplinary boundaries. Highly recommended. Graduates through professionals.
-CHOICE, January 2002

This book is a result of a successful, interdisciplinary collaboration between a statistician and a biologist. Most chapters are broken into two clearly identified parts-the first part is strongly rooted in biological applications and the second part contains the accompanying formal mathematical analyses. Despite the advanced level of this monograph, the writing is clear and well organized. The book is a highly recommended resource for scholars who are interested in mathematical and statistical analyses of shape information.
-Journal of Mathematical Psychology, Vol. 46 (2002)

This book describes statistical methods that are applicable to analyse morphometric data. ...The closing part offers new ideas to extend Euclidian distance matrix analysis procedures to complex biological problems. The book is an important practical guide for the analysis of morphometric data.
- Zentralblatt fur Mathematik, August 2002

...this is a useful and complementary addition to the recent series of books on statistical shape analysis.
-I. L. Dryden, Biometrics, Vol 58, June 2002

This book is an unusual book in that it is a collaborative work by a statistician and an anthropologist. ... useful for applied statisticians who are interested in analyzing the shapes of biological organisms.
- Technometrics, August 2004, Vol. 46, No. 3

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Book Description Taylor Francis Ltd, United States, 2001. Hardback. Book Condition: New. Language: English . This book usually ship within 10-15 business days and we will endeavor to dispatch orders quicker than this where possible. Brand New Book. 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. Bookseller Inventory # BTE9780849303197

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