000			03278nam a22003858i 4500
001			CR9781139094764
003			UkCbUP
005			20200124160234.0
006			m|||||o||d||||||||
007			cr||||||||||||
008			110607s2012||||enk o ||1 0|eng|d
020			_a9781139094764 (ebook)
020			_z9781107019584 (hardback)
020			_z9781107484313 (paperback)
040			_aUkCbUP _beng _erda _cUkCbUP
050		4	_aQA278.8 _b.B52 2012
082	0	4	_a519.5 _223
100	1		_aBhattacharya, Abhishek, _eauthor.
245	1	0	_aNonparametric inference on manifolds : _bwith applications to shape spaces / _cAbhishek Bhattacharya, Rabi Bhattacharya.
264		1	_aCambridge : _bCambridge University Press, _c2012.
300			_a1 online resource (xiii, 237 pages) : _bdigital, PDF file(s).
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
490	1		_aInstitute of Mathematical Statistics monographs ; _v2
500			_aTitle from publisher's bibliographic system (viewed on 05 Oct 2015).
505	0		_aIntroduction -- Examples -- Location and spread on metric spaces -- Extrinsic analysis on manifolds -- Intrinsic analysis on manifolds -- Landmark-based shape spaces -- Kendall's similarity shape spaces [characters omitted] -- The planar shape space [characters omitted] -- Reflection similarity shape spaces R[characters omitted] -- Stiefel manifolds V[characters omitted] -- Affine shape spaces A[characters omitted] -- Real projective spaces and projective shape spaces -- Nonparametric Bayes inference on manifolds -- Nonparametric Bayes regression, classification and hypothesis testing on manifolds -- Appendixes: A. Differentiable manifolds -- B. Riemannian manifolds -- C. Dirichlet processes -- D. Parametric models on S[character omitted] and [characters omitted].
520			_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		0	_aNonparametric statistics.
650		0	_aManifolds (Mathematics)
700	1		_aBhattacharya, R. N. _q(Rabindra Nath), _d1937- _eauthor.
776	0	8	_iPrint version: _z9781107019584
830		0	_aInstitute of Mathematical Statistics monographs ; _v2.
856	4	0	_uhttps://doi.org/10.1017/CBO9781139094764
999			_c517855 _d517853