Functional and Shape Data Analysis

Author: Anuj Srivastava,Eric P. Klassen

Publisher: Springer

ISBN: 1493940201

Category: Mathematics

Page: 447

View: 5817

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This textbook for courses on function data analysis and shape data analysis describes how to define, compare, and mathematically represent shapes, with a focus on statistical modeling and inference. It is aimed at graduate students in analysis in statistics, engineering, applied mathematics, neuroscience, biology, bioinformatics, and other related areas. The interdisciplinary nature of the broad range of ideas covered—from introductory theory to algorithmic implementations and some statistical case studies—is meant to familiarize graduate students with an array of tools that are relevant in developing computational solutions for shape and related analyses. These tools, gleaned from geometry, algebra, statistics, and computational science, are traditionally scattered across different courses, departments, and disciplines; Functional and Shape Data Analysis offers a unified, comprehensive solution by integrating the registration problem into shape analysis, better preparing graduate students for handling future scientific challenges. Recently, a data-driven and application-oriented focus on shape analysis has been trending. This text offers a self-contained treatment of this new generation of methods in shape analysis of curves. Its main focus is shape analysis of functions and curves—in one, two, and higher dimensions—both closed and open. It develops elegant Riemannian frameworks that provide both quantification of shape differences and registration of curves at the same time. Additionally, these methods are used for statistically summarizing given curve data, performing dimension reduction, and modeling observed variability. It is recommended that the reader have a background in calculus, linear algebra, numerical analysis, and computation.
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Applied Functional Data Analysis

Methods and Case Studies

Author: J.O. Ramsay,B.W. Silverman

Publisher: Springer

ISBN: 0387224653

Category: Mathematics

Page: 191

View: 8561

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This book contains the ideas of functional data analysis by a number of case studies. The case studies are accessible to research workers in a wide range of disciplines. Every reader should gain not only a specific understanding of the methods of functional data analysis, but more importantly a general insight into the underlying patterns of thought. There is an associated web site with MATLABr and S?PLUSr implementations of the methods discussed.
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Missing and Modified Data in Nonparametric Estimation

With R Examples

Author: Sam Efromovich

Publisher: CRC Press

ISBN: 1351679848

Category: Law

Page: 448

View: 1363

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This book presents a systematic and unified approach for modern nonparametric treatment of missing and modified data via examples of density and hazard rate estimation, nonparametric regression, filtering signals, and time series analysis. All basic types of missing at random and not at random, biasing, truncation, censoring, and measurement errors are discussed, and their treatment is explained. Ten chapters of the book cover basic cases of direct data, biased data, nondestructive and destructive missing, survival data modified by truncation and censoring, missing survival data, stationary and nonstationary time series and processes, and ill-posed modifications. The coverage is suitable for self-study or a one-semester course for graduate students with a prerequisite of a standard course in introductory probability. Exercises of various levels of difficulty will be helpful for the instructor and self-study. The book is primarily about practically important small samples. It explains when consistent estimation is possible, and why in some cases missing data should be ignored and why others must be considered. If missing or data modification makes consistent estimation impossible, then the author explains what type of action is needed to restore the lost information. The book contains more than a hundred figures with simulated data that explain virtually every setting, claim, and development. The companion R software package allows the reader to verify, reproduce and modify every simulation and used estimators. This makes the material fully transparent and allows one to study it interactively. Sam Efromovich is the Endowed Professor of Mathematical Sciences and the Head of the Actuarial Program at the University of Texas at Dallas. He is well known for his work on the theory and application of nonparametric curve estimation and is the author of Nonparametric Curve Estimation: Methods, Theory, and Applications. Professor Sam Efromovich is a Fellow of the Institute of Mathematical Statistics and the American Statistical Association.
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Recent Advances in Functional Data Analysis and Related Topics

Author: Frédéric Ferraty

Publisher: Springer Science & Business Media

ISBN: 9783790827361

Category: Mathematics

Page: 322

View: 4761

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New technologies allow us to handle increasingly large datasets, while monitoring devices are becoming ever more sophisticated. This high-tech progress produces statistical units sampled over finer and finer grids. As the measurement points become closer, the data can be considered as observations varying over a continuum. This intrinsic continuous data (called functional data) can be found in various fields of science, including biomechanics, chemometrics, econometrics, environmetrics, geophysics, medicine, etc. The failure of standard multivariate statistics to analyze such functional data has led the statistical community to develop appropriate statistical methodologies, called Functional Data Analysis (FDA). Today, FDA is certainly one of the most motivating and popular statistical topics due to its impact on crucial societal issues (health, environment, etc). This is why the FDA statistical community is rapidly growing, as are the statistical developments . Therefore, it is necessary to organize regular meetings in order to provide a state-of-art review of the recent advances in this fascinating area. This book collects selected and extended papers presented at the second International Workshop of Functional and Operatorial Statistics (Santander, Spain, 16-18 June, 2011), in which many outstanding experts on FDA will present the most relevant advances in this pioneering statistical area. Undoubtedly, these proceedings will be an essential resource for academic researchers, master students, engineers, and practitioners not only in statistics but also in numerous related fields of application.
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Geometry Driven Statistics

Author: Ian L. Dryden,John T. Kent

Publisher: John Wiley & Sons

ISBN: 1118866576

Category: Mathematics

Page: 432

View: 4590

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A timely collection of advanced, original material in the area of statistical methodology motivated by geometric problems, dedicated to the influential work of Kanti V. Mardia This volume celebrates Kanti V. Mardia′s long and influential career in statistics. A common theme unifying much of Mardia s work is the importance of geometry in statistics, and to highlight the areas emphasized in his research this book brings together 16 contributions from high–profile researchers in the field. Geometry Driven Statistics covers a wide range of application areas including directional data, shape analysis, spatial data, climate science, fingerprints, image analysis, computer vision and bioinformatics. The book will appeal to statisticians and others with an interest in data motivated by geometric considerations. Summarizing the state of the art, examining some new developments and presenting a vision for the future, Geometry Driven Statistics will enable the reader to broaden knowledge of important research areas in statistics and gain a new appreciation of the work and influence of Kanti V. Mardia.
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Functional Data Analysis

Author: Jim Ramsay,James Ramsay,B. W. Silverman

Publisher: Springer Science & Business Media

ISBN: 9780387400808

Category: Mathematics

Page: 426

View: 4672

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This is the second edition of a highly succesful book which has sold nearly 3000 copies world wide since its publication in 1997. Many chapters will be rewritten and expanded due to a lot of progress in these areas since the publication of the first edition. Bernard Silverman is the author of two other books, each of which has lifetime sales of more than 4000 copies. He has a great reputation both as a researcher and an author. This is likely to be the bestselling book in the Springer Series in Statistics for a couple of years.
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Progress in Advanced Structural and Functional Materials Design

Author: Tomoyuki Kakeshita

Publisher: Springer Science & Business Media

ISBN: 4431540644

Category: Technology & Engineering

Page: 290

View: 7425

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This book describes clearly various research topics investigated for these 10 years in the Research Center of Advanced Structural and Functional Materials Design in Osaka University, Japan. Every chapter is aimed at understanding most advanced researches in materials science by describing its fundamentals and details as much as possible. Since both general explanations and cutting-edge commentaries are given for each topic in this book, it provides a lot of useful information for ordinary readers as well as materials scientists & engineers who wish to understand the future development in materials science fields of metals, alloys, ceramics, semiconductors etc. In particular, this book deals with special fusion area of structural and functional materials such as medical bone materials, of which contents are very unique features as materials science textbook.
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Methods for Statistical Data Analysis of Multivariate Observations

Author: R. Gnanadesikan,Ram Gnanadesikan

Publisher: John Wiley & Sons

ISBN: 9780471161196

Category: Mathematics

Page: 353

View: 7828

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A practical guide for multivariate statistical techniques—now updated and revised In recent years, innovations in computer technology andstatistical methodologies have dramatically altered the landscapeof multivariate data analysis. This new edition of Methods forStatistical Data Analysis of Multivariate Observations explorescurrent multivariate concepts and techniques while retaining thesame practical focus of its predecessor. It integrates methods anddata-based interpretations relevant to multivariate analysis in away that addresses real-world problems arising in many areas ofinterest. Greatly revised and updated, this Second Edition provideshelpful examples, graphical orientation, numerous illustrations,and an appendix detailing statistical software, including the S (orSplus) and SAS systems. It also offers An expanded chapter on cluster analysis that covers advances inpattern recognition New sections on inputs to clustering algorithms and aids forinterpreting the results of cluster analysis An exploration of some new techniques of summarization andexposure New graphical methods for assessing the separations among theeigenvalues of a correlation matrix and for comparing sets ofeigenvectors Knowledge gained from advances in robust estimation anddistributional models that are slightly broader than themultivariate normal This Second Edition is invaluable for graduate students, appliedstatisticians, engineers, and scientists wishing to usemultivariate techniques in a variety of disciplines.
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Statistical Atlases and Computational Models of the Heart - Imaging and Modelling Challenges

5th International Workshop, STACOM 2014, Held in Conjunction with MICCAI 2014, Boston, MA, USA, September 18, 2014, Revised Selected Papers

Author: Oscar Camara,Tommaso Mansi,Mihaela Pop,Kawal Rhode,Maxime Sermesant,Alistair Young

Publisher: Springer

ISBN: 3319146785

Category: Computers

Page: 296

View: 3790

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This book constitutes the thoroughly refereed post-conference proceedings of the 5th International Workshop on Statistical Atlases and Computational Models of the Heart: Imaging and Modelling Challenges, STACOM 2014, held in conjunction with MICCAI 2014, in Boston, MA, USA, in September 2014. The 30 revised full papers were carefully reviewed and selected from numerous submissions. The papers cover a wide range of topics such as sections on cardiac image processing; atlas construction; statistical modelling of cardiac function across different patient populations; cardiac mapping; cardiac computational physiology; model customization; atlas based functional analysis; ontological schemata for data and results; integrated functional and structural analyses; as well as the pre-clinical and clinical applicability of these methods.
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Geomathematics: Theoretical Foundations, Applications and Future Developments

Author: Frits Agterberg

Publisher: Springer

ISBN: 3319068741

Category: Science

Page: 553

View: 6348

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This book provides a wealth of geomathematical case history studies performed by the author during his career at the Ministry of Natural Resources Canada, Geological Survey of Canada (NRCan-GSC). Several of the techniques newly developed by the author and colleagues that are described in this book have become widely adopted, not only for further research by geomathematical colleagues, but by government organizations and industry worldwide. These include Weights-of-Evidence modelling, mineral resource estimation technology, trend surface analysis, automatic stratigraphic correlation and nonlinear geochemical exploration methods. The author has developed maximum likelihood methodology and spline-fitting techniques for the construction of the international numerical geologic timescale. He has introduced the application of new theory of fractals and multi fractals in the geostatistical evaluation of regional mineral resources and ore reserves and to study the spatial distribution of metals in rocks. The book also contains sections deemed important by the author but that have not been widely adopted because they require further research. These include the geometry of preferred orientations of contours and edge effects on maps, time series analysis of Quaternary retreating ice sheet related sedimentary data, estimation of first and last appearances of fossil taxa from frequency distributions of their observed first and last occurrences, tectonic reactivation along pre-existing schistosity planes in fold belts, use of the grouped jackknife method for bias reduction in geometrical extrapolations and new applications of the theory of permanent, volume-independent frequency distributions.
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