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portada nonparametric inference on manifolds
Type
Physical Book
Author
Publisher
Language
English
Format
Hardcover
Dimensions
23.1x15.2x2 cm
Weight
0.52 kg.
ISBN
1107019583
ISBN13
9781107019584
Categories

nonparametric inference on manifolds

Abhishek Bhattacharya (Author) · Rabi Bhattacharya (Author) · Cambridge University Press · Hardcover

nonparametric inference on manifolds - Bhattacharya, Abhishek ; Bhattacharya, Rabi

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Synopsis "nonparametric inference on manifolds"

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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