Nonparametric Inference on Manifolds: With Applications to Shape Spaces - Couverture rigide

Bhattacharya, Abhishek; Bhattacharya, Rabi

 
9781107019584: Nonparametric Inference on Manifolds: With Applications to Shape Spaces
Couverture rigide
ISBN 10 : 1107019583 ISBN 13 : 9781107019584
Editeur : Cambridge University Press, 2012

Synopsis

This book introduces in a systematic manner a general nonparametric theory of statistics on manifolds, with emphasis on manifolds of shapes. The theory has important and varied applications in medical diagnostics, image analysis, and machine vision. An early chapter of examples establishes the effectiveness of the new methods and demonstrates how they outperform their parametric counterparts. Inference is developed for both intrinsic and extrinsic Fréchet means of probability distributions on manifolds, then applied to shape spaces defined as orbits of landmarks under a Lie group of transformations - in particular, similarity, reflection similarity, affine and projective transformations. In addition, nonparametric Bayesian theory is adapted and extended to manifolds for the purposes of density estimation, regression and classification. Ideal for statisticians who analyze manifold data and wish to develop their own methodology, this book is also of interest to probabilists, mathematicians, computer scientists, and morphometricians with mathematical training.

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À propos des auteurs

Abhishek Bhattacharya is currently working as an assistant professor at the Indian Statistical Institute. After gaining BStat and MStat degrees from the Institute in 2002 and 2004 respectively, and a PhD from the University of Arizona in 2008, he was a postdoctoral researcher at Duke University until the end of 2010, before joining ISI in 2011. Before writing this book, he published several articles in areas as diverse as nonparametric frequentist and Bayesian statistics on non-Euclidean manifolds. All those articles can be accessed from his website.

Rabi Bhattacharya is Professor in the Department of Mathematics at the University of Arizona, Tucson.

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
Cambridge University Press
Date d'édition
2012
Langue
anglais
ISBN 10 
1107019583
ISBN 13 
9781107019584
Reliure
Relié
Nombre de pages
252
Coordonnées du fabricant
non disponible
Personne responsable
Avery
https://www.avery.fr/

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France

Autres éditions populaires du même titre

9781107484313: Nonparametric Inference on Manifolds

Edition présentée

ISBN 10 :  1107484316 ISBN 13 :  9781107484313
Editeur : Cambridge University Press, 2015
Couverture souple