Differential Geometry and Statistics

Author: M.K. Murray

Publisher: Routledge

ISBN: 1351455117

Category: Mathematics

Page: 288

View: 7686

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Several years ago our statistical friends and relations introduced us to the work of Amari and Barndorff-Nielsen on applications of differential geometry to statistics. This book has arisen because we believe that there is a deep relationship between statistics and differential geometry and moreoever that this relationship uses parts of differential geometry, particularly its 'higher-order' aspects not readily accessible to a statistical audience from the existing literature. It is, in part, a long reply to the frequent requests we have had for references on differential geometry! While we have not gone beyond the path-breaking work of Amari and Barndorff- Nielsen in the realm of applications, our book gives some new explanations of their ideas from a first principles point of view as far as geometry is concerned. In particular it seeks to explain why geometry should enter into parametric statistics, and how the theory of asymptotic expansions involves a form of higher-order differential geometry. The first chapter of the book explores exponential families as flat geometries. Indeed the whole notion of using log-likelihoods amounts to exploiting a particular form of flat space known as an affine geometry, in which straight lines and planes make sense, but lengths and angles are absent. We use these geometric ideas to introduce the notion of the second fundamental form of a family whose vanishing characterises precisely the exponential families.
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Signal and Image Processing for Biometrics

Author: Jacob Scharcanski,Hugo Proença,Eliza Du

Publisher: Springer Science & Business Media

ISBN: 3642540805

Category: Technology & Engineering

Page: 331

View: 7875

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This volume offers a guide to the state of the art in the fast evolving field of biometric recognition to newcomers and experienced practitioners. It is focused on the emerging strategies to perform biometric recognition under uncontrolled data acquisition conditions. The mainstream research work in this field is presented in an organized manner, so the reader can easily follow the trends that best suits her/his interests in this growing field. The book chapters cover the recent advances in less controlled / covert data acquisition frameworks, segmentation of poor quality biometric data, biometric data quality assessment, normalization of poor quality biometric data. contactless biometric recognition strategies, biometric recognition robustness, data resolution, illumination, distance, pose, motion, occlusions, multispectral biometric recognition, multimodal biometrics, fusion at different levels, high confidence automatic surveillance.
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Stochastic Analysis and Applications

Proceedings of the Fifth Gregynog Symposium

Author: I M Davies,A Truman,K D Elworthy

Publisher: World Scientific

ISBN: 9814548111

Category:

Page: 520

View: 2286

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This volume contains papers which were presented at a meeting entitled “Stochastic Analysis and Applications“ held at Gregynog Hall, Powys, from the 9th — 14th July 1995. The meeting consisted of a mixture of plenary/review talks and special interest sessions covering most of the current areas of activity in stochastic analysis. The meeting was jointly organized by the Department of Mathematics, University of Wales Swansea and the Mathematics Institute, University of Warwick in connection with the Stochastic Analysis year of activity. The papers contained herein are accessible to workers in the field of stochastic analysis and give a good coverage of topics of current interest in the research community. Contents:Logarithmic Sobolev Inequalities on Loop Spaces Over Compact Riemannian Manifolds (S Aida)Euclidean Random Fields, Pseudodifferential Operators, and Wightman Functions (S Albeverio et al)Strong Markov Processes and the Dirichlet Problem in von Neumann Algebras (S Attal & K R Parthasarathy)On the General Form of Quantum Stochastic Evolution Equation (V P Belavkin)Stochastic Flows of Diffeomorphisms (Z Brzezniak & K D Elworthy)Gromov's Hyperbolicity and Picard's Little Theorem for Harmonic Maps (M Cranston et al)On Heat Kernel Logarithmic Sobolev inequalities (B K Driver & Y Hu)Evolution Equations in the Theory of Statistical Manifolds (B Grigelionis)Stochastic Flows with Self-Similar Properties (H Kunita)Path Space of a Symplectic Manifold (R Léandre)The General Linear Stochastic Volterra Equation with Anticipating Coefficients (B Øksendal & T Zhang)Local Non Smooth Flows on the Wiener Space and Applications (G Peters)On Transformations of Measures Related to Second Order Differential Equations (V R Steblovskaya)Extension of Lipschitz Functions on Wiener Space (A S Üstünel & M Zakai)On Large Deviations for SDE Systems Without Bounded Coefficient Derivatives (A Y Veretennikov)Maupertius' Least Action Principle for Diffusions (J C Zambrini)Large Deviations Results Without Continuity Hypothesis on the Diffusion Term (W Zheng)and other papers Readership: Stochastic analysts, mathematical physicists and probabilists. keywords:
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Mathematical Theory of Statistics

Statistical Experiments and Asymptotic Decision Theory

Author: Helmut Strasser

Publisher: Walter de Gruyter

ISBN: 3110850826

Category: Mathematics

Page: 504

View: 2644

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The series is devoted to the publication of monographs and high-level textbooks in mathematics, mathematical methods and their applications. Apart from covering important areas of current interest, a major aim is to make topics of an interdisciplinary nature accessible to the non-specialist. The works in this series are addressed to advanced students and researchers in mathematics and theoretical physics. In addition, it can serve as a guide for lectures and seminars on a graduate level. The series de Gruyter Studies in Mathematics was founded ca. 30 years ago by the late Professor Heinz Bauer and Professor Peter Gabriel with the aim to establish a series of monographs and textbooks of high standard, written by scholars with an international reputation presenting current fields of research in pure and applied mathematics. While the editorial board of the Studies has changed with the years, the aspirations of the Studies are unchanged. In times of rapid growth of mathematical knowledge carefully written monographs and textbooks written by experts are needed more than ever, not least to pave the way for the next generation of mathematicians. In this sense the editorial board and the publisher of the Studies are devoted to continue the Studies as a service to the mathematical community. Please submit any book proposals to Niels Jacob.
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Metron

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Statistics

Page: N.A

View: 2410

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Includes list of publications received.
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A Course in Mathematical Statistics and Large Sample Theory

Author: Rabi Bhattacharya,Lizhen Lin,Victor Patrangenaru

Publisher: Springer

ISBN: 1493940325

Category: Mathematics

Page: 389

View: 2955

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This graduate-level textbook is primarily aimed at graduate students of statistics, mathematics, science, and engineering who have had an undergraduate course in statistics, an upper division course in analysis, and some acquaintance with measure theoretic probability. It provides a rigorous presentation of the core of mathematical statistics. Part I of this book constitutes a one-semester course on basic parametric mathematical statistics. Part II deals with the large sample theory of statistics - parametric and nonparametric, and its contents may be covered in one semester as well. Part III provides brief accounts of a number of topics of current interest for practitioners and other disciplines whose work involves statistical methods.
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