000			01579nam a22001577a 4500
008			180825b2012 xxu||||| |||| 00| 0 eng d
020			_a9781107484313
082			_a519.5 BHA-A
245			_aNonparametric inference on manifolds with applications to shape spaces / _cAbhishek Bhattacharya and Rabi Bhattacharya
260			_aUK _bCambridge University Press _c2012
300			_a237 P.
365			_aGBP _b27.99
500			_aThis 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.
650			_aNonparametric statistics
650			_aManifolds (Mathematics)
999			_c31442 _d31442