03095nam a22003498i 4500001001600000003000700016008004100023020001800064020001800082020001800100035002000118041000800138082001400146100003600160245013300196264007100329300004000400336002600440337002600466338003600492490005700528500001300585505077900598520107901377650003002456650002802486700003302514856005502547932003202602596000602634949010502640CR9781139094764UkCbUP110607s2012||||enk o ||1 0|eng|d a9781139094764 a9781107019584 a9781107484313 a(Sirsi) a799836 aeng04a519.52231 aBhattacharya, Abhishek,eauthor10aNonparametric inference on manifolds :bwith applications to shape spacesh[E-Book] /cAbhishek Bhattacharya, Rabi Bhattacharya. 1aCambridge :bCambridge University Press,c2012e(CUP)fCUP20200108 a1 online resource (xiii, 237 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier aInstitute of Mathematical Statistics monographs ;v2 aenglisch0 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]. 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. 0aNonparametric statistics. 0aManifolds (Mathematics)1 aBhattacharya, R. N.,eauthor40uhttps://doi.org/10.1017/CBO9781139094764zVolltext aCambridgeCore (Order 30059) a1 aXX(799836.1)wAUTOc1i799836-1001lELECTRONICmZBrNsYtE-BOOKu8/1/2020xUNKNOWNzUNKNOWN1ONLINE