Statistical Shape Analysis

This book is a significant update of the highly-regarded `Statistical Shape Analysis’ by the same authors.

Statistical Shape Analysis

A thoroughly revised and updated edition of this introduction to modern statistical methods for shape analysis Shape analysis is an important tool in the many disciplines where objects are compared using geometrical features. Examples include comparing brain shape in schizophrenia; investigating protein molecules in bioinformatics; and describing growth of organisms in biology. This book is a significant update of the highly-regarded `Statistical Shape Analysis’ by the same authors. The new edition lays the foundations of landmark shape analysis, including geometrical concepts and statistical techniques, and extends to include analysis of curves, surfaces, images and other types of object data. Key definitions and concepts are discussed throughout, and the relative merits of different approaches are presented. The authors have included substantial new material on recent statistical developments and offer numerous examples throughout the text. Concepts are introduced in an accessible manner, while retaining sufficient detail for more specialist statisticians to appreciate the challenges and opportunities of this new field. Computer code has been included for instructional use, along with exercises to enable readers to implement the applications themselves in R and to follow the key ideas by hands-on analysis. Statistical Shape Analysis: with Applications in R will offer a valuable introduction to this fast-moving research area for statisticians and other applied scientists working in diverse areas, including archaeology, bioinformatics, biology, chemistry, computer science, medicine, morphometics and image analysis .

Statistical Shape Analysis

With Applications in R Ian L. Dryden, Kanti V. Mardia ... Wiley also publishes its books in a variety of electronic formats. ... Other titles: Statistical shape analysis | Wiley series in probability and statistics.

Statistical Shape Analysis

A thoroughly revised and updated edition of this introduction to modern statistical methods for shape analysis Shape analysis is an important tool in the many disciplines where objects are compared using geometrical features. Examples include comparing brain shape in schizophrenia; investigating protein molecules in bioinformatics; and describing growth of organisms in biology. This book is a significant update of the highly-regarded `Statistical Shape Analysis’ by the same authors. The new edition lays the foundations of landmark shape analysis, including geometrical concepts and statistical techniques, and extends to include analysis of curves, surfaces, images and other types of object data. Key definitions and concepts are discussed throughout, and the relative merits of different approaches are presented. The authors have included substantial new material on recent statistical developments and offer numerous examples throughout the text. Concepts are introduced in an accessible manner, while retaining sufficient detail for more specialist statisticians to appreciate the challenges and opportunities of this new field. Computer code has been included for instructional use, along with exercises to enable readers to implement the applications themselves in R and to follow the key ideas by hands-on analysis. Statistical Shape Analysis: with Applications in R will offer a valuable introduction to this fast-moving research area for statisticians and other applied scientists working in diverse areas, including archaeology, bioinformatics, biology, chemistry, computer science, medicine, morphometics and image analysis .

Object Oriented Data Analysis

Statistical shape analysis with applications in R. Wiley Series in Probability and Statistics. John Wiley & Sons, Ltd., Chichester, second edition. pages 12, 68, 139, 141, 142, 158, 166, 167, 202, 225, 328, 329 Dryden, I. L., Pennec, ...

Object Oriented Data Analysis

Object Oriented Data Analysis is a framework that facilitates inter-disciplinary research through new terminology for discussing the often many possible approaches to the analysis of complex data. Such data are naturally arising in a wide variety of areas. This book aims to provide ways of thinking that enable the making of sensible choices. The main points are illustrated with many real data examples, based on the authors' personal experiences, which have motivated the invention of a wide array of analytic methods. While the mathematics go far beyond the usual in statistics (including differential geometry and even topology), the book is aimed at accessibility by graduate students. There is deliberate focus on ideas over mathematical formulas. J. S. Marron is the Amos Hawley Distinguished Professor of Statistics, Professor of Biostatistics, Adjunct Professor of Computer Science, Faculty Member of the Bioinformatics and Computational Biology Curriculum and Research Member of the Lineberger Cancer Center and the Computational Medicine Program, at the University of North Carolina, Chapel Hill. Ian L. Dryden is a Professor in the Department of Mathematics and Statistics at Florida International University in Miami, has served as Head of School of Mathematical Sciences at the University of Nottingham, and is joint author of the acclaimed book Statistical Shape Analysis.

Geometry and Statistics

Statistical Shape Analysis With Applications in R, second ed. Wiley Series in Probability and Statistics, Wiley, Chichester, UK; Hoboken, NJ, ISBN: 978-0-470-69962-1. Duchateau, N., De Craene, M., Piella, G., Silva, E., Doltra, A., ...

Geometry and Statistics

Geometry and Statistics, Volume 46 in the Handbook of Statistics series, highlights new advances in the field, with this new volume presenting interesting chapters written by an international board of authors. Provides the authority and expertise of leading contributors from an international board of authors Presents the latest release in the Handbook of Statistics series Updated release includes the latest information on Geometry and Statistics

Digital Anatomy

Applications of Virtual, Mixed and Augmented Reality Jean-François Uhl, Joaquim Jorge, Daniel Simões Lopes, ... Mardia KV (2016) Statistical shape analysis with applications in R. Wiley series in probability and statistics.

Digital Anatomy

This book offers readers fresh insights on applying Extended Reality to Digital Anatomy, a novel emerging discipline. Indeed, the way professors teach anatomy in classrooms is changing rapidly as novel technology-based approaches become ever more accessible. Recent studies show that Virtual (VR), Augmented (AR), and Mixed-Reality (MR) can improve both retention and learning outcomes. Readers will find relevant tutorials about three-dimensional reconstruction techniques to perform virtual dissections. Several chapters serve as practical manuals for students and trainers in anatomy to refresh or develop their Digital Anatomy skills. We developed this book as a support tool for collaborative efforts around Digital Anatomy, especially in distance learning, international and interdisciplinary contexts. We aim to leverage source material in this book to support new Digital Anatomy courses and syllabi in interdepartmental, interdisciplinary collaborations. Digital Anatomy – Applications of Virtual, Mixed and Augmented Reality provides a valuable tool to foster cross-disciplinary dialogues between anatomists, surgeons, radiologists, clinicians, computer scientists, course designers, and industry practitioners. It is the result of a multidisciplinary exercise and will undoubtedly catalyze new specialties and collaborative Master and Doctoral level courses world-wide. In this perspective, the UNESCO Chair in digital anatomy was created at the Paris Descartes University in 2015 (www.anatomieunesco.org). It aims to federate the education of anatomy around university partners from all over the world, wishing to use these new 3D modeling techniques of the human body.

Neural Information Processing

Dryden, I.L., Mardia, K.V.: Statistical Shape Analysis with Applications in R. Wiley Series in Probability and Statistics, 2nd edn. Wiley, Chichester (2016) 2. Ferrari, V.: ETHZ Shape Classes, September 2009.

Neural Information Processing

The seven-volume set of LNCS 11301-11307, constitutes the proceedings of the 25th International Conference on Neural Information Processing, ICONIP 2018, held in Siem Reap, Cambodia, in December 2018. The 401 full papers presented were carefully reviewed and selected from 575 submissions. The papers address the emerging topics of theoretical research, empirical studies, and applications of neural information processing techniques across different domains. The 4th volume, LNCS 11304, is organized in topical sections on feature selection, clustering, classification, and detection.

Discovery Science

We show that the proposed framework is robust and beneficial when the triplet comparisons are noisy. ... Dryden, I.L., Mardia, K.V.: Statistical shape analysis with applications in R. Wiley Series in Probability and Statistics, vol.

Discovery Science

This book constitutes the proceedings of the 24th International Conference on Discovery Science, DS 2021, which took place virtually during October 11-13, 2021. The 36 papers presented in this volume were carefully reviewed and selected from 76 submissions. The contributions were organized in topical sections named: applications; classification; data streams; graph and network mining; machine learning for COVID-19; neural networks and deep learning; preferences and recommender systems; representation learning and feature selection; responsible artificial intelligence; and spatial, temporal and spatiotemporal data.

Spatial Statistics Methodological Aspects and Applications

Statistical Shape Analysis. Wiley Series in Probability and Statistics: Probability and Statistics. New York: Wiley. Good, P. (1994). Permutation Tests. Springer Series in Statistics. New York: Springer. Goodall, C.R. (1991).

Spatial Statistics  Methodological Aspects and Applications

This volume contains presentations by eminent researchers: Statistical Inference for Spatial Processes; Image Analysis; Applications of Spatial Statistics in Earth, Environmental, and Health Sciences; and Statistics of Brain Mapping. They range from asymptotic considerations for spatial processes to practical considerations related to particular applications including important methodological aspects. Many contributions concern image analysis, mainly images related to brain mapping.

Linear Models and Time Series Analysis

The Wiley Series in Probability and Statistics is well established and authoritative. ... Robust Correlation: Theory and Applications by Georgy L. Shevlyakov, Hannu Oja August 2016 Statistical Shape Analysis: With Applications in R, ...

Linear Models and Time Series Analysis

A comprehensive and timely edition on an emerging new trend in time series Linear Models and Time-Series Analysis: Regression, ANOVA, ARMA and GARCH sets a strong foundation, in terms of distribution theory, for the linear model (regression and ANOVA), univariate time series analysis (ARMAX and GARCH), and some multivariate models associated primarily with modeling financial asset returns (copula-based structures and the discrete mixed normal and Laplace). It builds on the author's previous book, Fundamental Statistical Inference: A Computational Approach, which introduced the major concepts of statistical inference. Attention is explicitly paid to application and numeric computation, with examples of Matlab code throughout. The code offers a framework for discussion and illustration of numerics, and shows the mapping from theory to computation. The topic of time series analysis is on firm footing, with numerous textbooks and research journals dedicated to it. With respect to the subject/technology, many chapters in Linear Models and Time-Series Analysis cover firmly entrenched topics (regression and ARMA). Several others are dedicated to very modern methods, as used in empirical finance, asset pricing, risk management, and portfolio optimization, in order to address the severe change in performance of many pension funds, and changes in how fund managers work. Covers traditional time series analysis with new guidelines Provides access to cutting edge topics that are at the forefront of financial econometrics and industry Includes latest developments and topics such as financial returns data, notably also in a multivariate context Written by a leading expert in time series analysis Extensively classroom tested Includes a tutorial on SAS Supplemented with a companion website containing numerous Matlab programs Solutions to most exercises are provided in the book Linear Models and Time-Series Analysis: Regression, ANOVA, ARMA and GARCH is suitable for advanced masters students in statistics and quantitative finance, as well as doctoral students in economics and finance. It is also useful for quantitative financial practitioners in large financial institutions and smaller finance outlets.

Data Science for Nano Image Analysis

Advances in Applied Probability 23:259–276 Dryden IL, Mardia KV (1998) Statistical Shape Analysis. John Wiley & Sons, West Sussex, UK Dryden IL, Mardia KV (2016) Statistical Shape Analysis: With Applications in R, 2nd Edition.

Data Science for Nano Image Analysis

This book combines two distinctive topics: data science/image analysis and materials science. The purpose of this book is to show what type of nano material problems can be better solved by which set of data science methods. The majority of material science research is thus far carried out by domain-specific experts in material engineering, chemistry/chemical engineering, and mechanical & aerospace engineering. The book could benefit materials scientists and manufacturing engineers who were not exposed to systematic data science training while in schools, or data scientists in computer science or statistics disciplines who want to work on material image problems or contribute to materials discovery and optimization. This book provides in-depth discussions of how data science and operations research methods can help and improve nano image analysis, automating the otherwise manual and time-consuming operations for material engineering and enhancing decision making for nano material exploration. A broad set of data science methods are covered, including the representations of images, shape analysis, image pattern analysis, and analysis of streaming images, change points detection, graphical methods, and real-time dynamic modeling and object tracking. The data science methods are described in the context of nano image applications, with specific material science case studies.

Introduction to Time Series Analysis and Forecasting

Edition DASU and JOHNSON r Exploratory Data Mining and Data Cleaning DAVID and NAGARAJA r Order Statistics, ... and STUDDEN r The Theory of Canonical Moments with Applications in Statistics, Probability, and Analysis DEY and MUKERJEE r ...

Introduction to Time Series Analysis and Forecasting

Praise for the First Edition "…[t]he book is great for readers who need to applythe methods and models presented but have little background inmathematics and statistics." -MAA Reviews Thoroughly updated throughout, Introduction to Time SeriesAnalysis and Forecasting, Second Edition presents theunderlying theories of time series analysis that are needed toanalyze time-oriented data and construct real-world short- tomedium-term statistical forecasts. Authored by highly-experienced academics and professionals inengineering statistics, the Second Edition featuresdiscussions on both popular and modern time series methodologies aswell as an introduction to Bayesian methods in forecasting.Introduction to Time Series Analysis and Forecasting, SecondEdition also includes: Over 300 exercises from diverse disciplines including healthcare, environmental studies, engineering, and finance More than 50 programming algorithms using JMP®, SAS®,and R that illustrate the theory and practicality of forecastingtechniques in the context of time-oriented data New material on frequency domain and spatial temporaldata analysis Expanded coverage of the variogram and spectrum withapplications as well as transfer and intervention modelfunctions A supplementary website featuring PowerPoint®slides, data sets, and select solutions to the problems Introduction to Time Series Analysis and Forecasting, SecondEdition is an ideal textbook upper-undergraduate andgraduate-levels courses in forecasting and time series. The book isalso an excellent reference for practitioners and researchers whoneed to model and analyze time series data to generate forecasts.

A Primer on Experiments with Mixtures

CHATTERJEE and HADI r Sensitivity Analysis in Linear Regression CHERNICK r Bootstrap Methods: A Guide for ... Second Edition CLARKE r Linear Models: The Theory and Application of Analysis of Variance CLARKE and DISNEY r Probability and ...

A Primer on Experiments with Mixtures

The concise yet authoritative presentation of key techniques for basic mixtures experiments Inspired by the author's bestselling advanced book on the topic, A Primer on Experiments with Mixtures provides an introductory presentation of the key principles behind experimenting with mixtures. Outlining useful techniques through an applied approach with examples from real research situations, the book supplies a comprehensive discussion of how to design and set up basic mixture experiments, then analyze the data and draw inferences from results. Drawing from his extensive experience teaching the topic at various levels, the author presents the mixture experiments in an easy-to-follow manner that is void of unnecessary formulas and theory. Succinct presentations explore key methods and techniques for carrying out basic mixture experiments, including: Designs and models for exploring the entire simplex factor space, with coverage of simplex-lattice and simplex-centroid designs, canonical polynomials, the plotting of individual residuals, and axial designs Multiple constraints on the component proportions in the form of lower and/or upper bounds, introducing L-Pseudocomponents, multicomponent constraints, and multiple lattice designs for major and minor component classifications Techniques for analyzing mixture data such as model reduction and screening components, as well as additional topics such as measuring the leverage of certain design points Models containing ratios of the components, Cox's mixture polynomials, and the fitting of a slack variable model A review of least squares and the analysis of variance for fitting data Each chapter concludes with a summary and appendices with details on the technical aspects of the material. Throughout the book, exercise sets with selected answers allow readers to test their comprehension of the material, and References and Recommended Reading sections outline further resources for study of the presented topics. A Primer on Experiments with Mixtures is an excellent book for one-semester courses on mixture designs and can also serve as a supplement for design of experiments courses at the upper-undergraduate and graduate levels. It is also a suitable reference for practitioners and researchers who have an interest in experiments with mixtures and would like to learn more about the related mixture designs and models.

Generalized Linear and Mixed Models

Charles E. McCulloch, Shayle R. Searle ... Stuart Hunter, Emeritus, David G. Kendall, Emeritus Probability and Statistics Section *ANDERSON - The Statistical Analysis of Time Series ARNOLD, BALAKRISHNAN, and NAGARAJA ' A First Course in ...

Generalized  Linear  and Mixed Models

Wiley Series in Probability and Statistics A modern perspective on mixed models The availability of powerful computing methods in recent decades has thrust linear and nonlinear mixed models into the mainstream of statistical application. This volume offers a modern perspective on generalized, linear, and mixed models, presenting a unified and accessible treatment of the newest statistical methods for analyzing correlated, nonnormally distributed data. As a follow-up to Searle's classic, Linear Models, and Variance Components by Searle, Casella, and McCulloch, this new work progresses from the basic one-way classification to generalized linear mixed models. A variety of statistical methods are explained and illustrated, with an emphasis on maximum likelihood and restricted maximum likelihood. An invaluable resource for applied statisticians and industrial practitioners, as well as students interested in the latest results, Generalized, Linear, and Mixed Models features: * A review of the basics of linear models and linear mixed models * Descriptions of models for nonnormal data, including generalized linear and nonlinear models * Analysis and illustration of techniques for a variety of real data sets * Information on the accommodation of longitudinal data using these models * Coverage of the prediction of realized values of random effects * A discussion of the impact of computing issues on mixed models

Geometric Structures of Statistical Physics Information Geometry and Learning

Bertinet, A., Agnan, T.C.: Reproducing Kernel Hilbert Spaces in Probability and Statistics. ... Dryden, I.L., Mardia, K.V.: Statistical shape analysis, with applications in R, 2nd edn. John Wiley and Sons, Chichester (2016) 11.

Geometric Structures of Statistical Physics  Information Geometry  and Learning

Machine learning and artificial intelligence increasingly use methodological tools rooted in statistical physics. Conversely, limitations and pitfalls encountered in AI question the very foundations of statistical physics. This interplay between AI and statistical physics has been attested since the birth of AI, and principles underpinning statistical physics can shed new light on the conceptual basis of AI. During the last fifty years, statistical physics has been investigated through new geometric structures allowing covariant formalization of the thermodynamics. Inference methods in machine learning have begun to adapt these new geometric structures to process data in more abstract representation spaces. This volume collects selected contributions on the interplay of statistical physics and artificial intelligence. The aim is to provide a constructive dialogue around a common foundation to allow the establishment of new principles and laws governing these two disciplines in a unified manner. The contributions were presented at the workshop on the Joint Structures and Common Foundation of Statistical Physics, Information Geometry and Inference for Learning which was held in Les Houches in July 2020. The various theoretical approaches are discussed in the context of potential applications in cognitive systems, machine learning, signal processing.

Brain Body and Machine

Dryden, I.L., Mardia, K.V.: Statistical shape analysis. Wiley Series in Probability and Statistics. John Wiley & Sons Ltd., Chichester (1998) 9. Siddiqi, K., Pizer, S.M.: Medial Representations: Mathematics, Algorithms and Applications.

Brain  Body and Machine

The reader will find here papers on human-robot interaction as well as human safety algorithms; haptic interfaces; innovative instruments and algorithms for the sensing of motion and the identification of brain neoplasms; even a paper on a saxophone-playing robot.

Statistical Intervals

Wiley. Series. in. Probability. and. Statistics. Statistical Intervals: A Guide for Practitioners and Researchers, ... 2nd Edition by Marvin H. J. Gruber, Shayle R. Searle Statistical Shape Analysis: With Applications in R, ...

Statistical Intervals

Describes statistical intervals to quantify sampling uncertainty,focusing on key application needs and recently developed methodology in an easy-to-apply format Statistical intervals provide invaluable tools for quantifying sampling uncertainty. The widely hailed first edition, published in 1991, described the use and construction of the most important statistical intervals. Particular emphasis was given to intervals—such as prediction intervals, tolerance intervals and confidence intervals on distribution quantiles—frequently needed in practice, but often neglected in introductory courses. Vastly improved computer capabilities over the past 25 years have resulted in an explosion of the tools readily available to analysts. This second edition—more than double the size of the first—adds these new methods in an easy-to-apply format. In addition to extensive updating of the original chapters, the second edition includes new chapters on: Likelihood-based statistical intervals Nonparametric bootstrap intervals Parametric bootstrap and other simulation-based intervals An introduction to Bayesian intervals Bayesian intervals for the popular binomial, Poisson and normal distributions Statistical intervals for Bayesian hierarchical models Advanced case studies, further illustrating the use of the newly described methods New technical appendices provide justification of the methods and pathways to extensions and further applications. A webpage directs readers to current readily accessible computer software and other useful information. Statistical Intervals: A Guide for Practitioners and Researchers, Second Edition is an up-to-date working guide and reference for all who analyze data, allowing them to quantify the uncertainty in their results using statistical intervals.

Foundations of Linear and Generalized Linear Models

DEMIDENKO r Mixed Models: Theory and Applications with R, Second Edition DENISON, HOLMES, MALLICK, and SMITH r ... Third Edition DRYDEN and MARDIA r Statistical Shape Analysis DUDEWICZ and MISHRA r Modern Mathematical Statistics DUNN ...

Foundations of Linear and Generalized Linear Models

A valuable overview of the most important ideas and results in statistical modeling Written by a highly-experienced author, Foundations of Linear and Generalized Linear Models is a clear and comprehensive guide to the key concepts and results of linearstatistical models. The book presents a broad, in-depth overview of the most commonly usedstatistical models by discussing the theory underlying the models, R software applications,and examples with crafted models to elucidate key ideas and promote practical modelbuilding. The book begins by illustrating the fundamentals of linear models, such as how the model-fitting projects the data onto a model vector subspace and how orthogonal decompositions of the data yield information about the effects of explanatory variables. Subsequently, the book covers the most popular generalized linear models, which include binomial and multinomial logistic regression for categorical data, and Poisson and negative binomial loglinear models for count data. Focusing on the theoretical underpinnings of these models, Foundations ofLinear and Generalized Linear Models also features: An introduction to quasi-likelihood methods that require weaker distributional assumptions, such as generalized estimating equation methods An overview of linear mixed models and generalized linear mixed models with random effects for clustered correlated data, Bayesian modeling, and extensions to handle problematic cases such as high dimensional problems Numerous examples that use R software for all text data analyses More than 400 exercises for readers to practice and extend the theory, methods, and data analysis A supplementary website with datasets for the examples and exercises An invaluable textbook for upper-undergraduate and graduate-level students in statistics and biostatistics courses, Foundations of Linear and Generalized Linear Models is also an excellent reference for practicing statisticians and biostatisticians, as well as anyone who is interested in learning about the most important statistical models for analyzing data.

Reliability

Modeling, Prediction, and Optimization Wallace R. Blischke, D. N. Prabhakar Murthy ... Stuart Hunter, Emeritus Probability and Statistics Section *ANDERSON - The Statistical Analysis of Time Series ARNOLD, BALAKRISHNAN, and NAGARAJA - A ...

Reliability

Bringing together business and engineering to reliability analysisWith manufactured products exploding in numbers and complexity,reliability studies play an increasingly critical role throughout aproduct's entire life cycle-from design to post-sale support.Reliability: Modeling, Prediction, and Optimization presents aremarkably broad framework for the analysis of the technical andcommercial aspects of product reliability, integrating concepts andmethodologies from such diverse areas as engineering, materialsscience, statistics, probability, operations research, andmanagement. Written in plain language by two highly respectedexperts in the field, this practical work provides engineers,operations managers, and applied statisticians with bothqualitative and quantitative tools for solving a variety ofcomplex, real-world reliability problems. A wealth of examples andcase studies accompanies: * Comprehensive coverage of assessment, prediction, and improvementat each stage of a product's life cycle * Clear explanations of modeling and analysis for hardware rangingfrom a single part to whole systems * Thorough coverage of test design and statistical analysis ofreliability data * A special chapter on software reliability * Coverage of effective management of reliability, product support,testing, pricing, and related topics * Lists of sources for technical information, data, and computerprograms * Hundreds of graphs, charts, and tables, as well as over 500references * PowerPoint slides are available from the Wiley editorialdepartment.

Bayesian Analysis of Stochastic Process Models

... LANZA r Latent Class and Latent Transition Analysis: With Applications in the Social, Behavioral, and Health Sciences CONGDON r Applied Bayesian Modelling CONGDON r Bayesian Models for Categorical Data CONGDON r Bayesian Statistical ...

Bayesian Analysis of Stochastic Process Models

Bayesian analysis of complex models based on stochastic processes has in recent years become a growing area. This book provides a unified treatment of Bayesian analysis of models based on stochastic processes, covering the main classes of stochastic processing including modeling, computational, inference, forecasting, decision making and important applied models. Key features: Explores Bayesian analysis of models based on stochastic processes, providing a unified treatment. Provides a thorough introduction for research students. Computational tools to deal with complex problems are illustrated along with real life case studies Looks at inference, prediction and decision making. Researchers, graduate and advanced undergraduate students interested in stochastic processes in fields such as statistics, operations research (OR), engineering, finance, economics, computer science and Bayesian analysis will benefit from reading this book. With numerous applications included, practitioners of OR, stochastic modelling and applied statistics will also find this book useful.

Bayesian Estimation and Inference in Computational Anatomy and Neuroimaging Methods Applications

3, 1102–1123. doi:10.1214/09-AOAS249 Dryden, I. L., and Mardia, K. V. (1998). Statistical Shape Analysis. Wiley Series in Probability and Statistics: Probability and Statistics. Chichester: John Wiley & Sons, Ltd. Eguíluz, V. M., ...

Bayesian Estimation and Inference in Computational Anatomy and Neuroimaging  Methods   Applications

Computational Anatomy (CA) is an emerging discipline aiming to understand anatomy by utilizing a comprehensive set of mathematical tools. CA focuses on providing precise statistical encodings of anatomy with direct application to a broad range of biological and medical settings. During the past two decades, there has been an ever-increasing pace in the development of neuroimaging techniques, delivering in vivo information on the anatomy and physiological signals of different human organs through a variety of imaging modalities such as MRI, x-ray, CT, and PET. These multi-modality medical images provide valuable data for accurate interpretation and estimation of various biological parameters such as anatomical labels, disease types, cognitive states, functional connectivity between distinct anatomical regions, as well as activation responses to specific stimuli. In the era of big neuroimaging data, Bayes’ theorem provides a powerful tool to deliver statistical conclusions by combining the current information and prior experience. When sufficiently good data is available, Bayes’ theorem can utilize it fully and provide statistical inferences/estimations with the least error rate. Bayes’ theorem arose roughly three hundred years ago and has seen extensive application in many fields of science and technology, including recent neuroimaging, ever since. The last fifteen years have seen a great deal of success in the application of Bayes’ theorem to the field of CA and neuroimaging. That said, given that the power and success of Bayes’ rule largely depends on the validity of its probabilistic inputs, it is still a challenge to perform Bayesian estimation and inference on the typically noisy neuroimaging data of the real world. We assembled contributions focusing on recent developments in CA and neuroimaging through Bayesian estimation and inference, in terms of both methodologies and applications. It is anticipated that the articles in this Research Topic will provide a greater insight into the field of Bayesian imaging analysis.