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Multivariate Analysis of Ecological Data using Canoco 5

This revised and updated edition focuses on constrained ordination (RDA, CCA), variation partitioning and the use of permutation tests of statistical hypotheses about multivariate data. Both classification and modern regression methods (GLM, GAM, loess) are reviewed and species functional traits and spatial structures analysed. Nine case studies of varying difficulty help to illustrate the suggested analytical methods, using the latest version of Canoco 5. All studies utilise descriptive and manipulative approaches, and are supported by data sets and project files available from the book website: http://regent. prf. jcu. cz/maed2/. Written primarily for community ecologists needing to analyse data resulting from field observations and experiments, this book is a valuable resource to students and researchers dealing with both simple and complex ecological problems, such as the variation of biotic communities with environmental conditions or their response to experimental manipulation.

Multivariate Analysis of Ecological Data with ade4

This book introduces the ade4 package for R which provides multivariate methods for the analysis of ecological data. It is implemented around the mathematical concept of the duality diagram, and provides a unified framework for multivariate analysis. The authors offer a detailed presentation of the theoretical framework of the duality diagram and also of its application to real-world ecological problems. These two goals may seem contradictory, as they concern two separate groups of scientists, namely statisticians and ecologists. However, statistical ecology has become a scientific discipline of its own, and the good use of multivariate data analysis methods by ecologists implies a fair knowledge of the mathematical properties of these methods.The organization of the book is based on ecological questions, but these questions correspond to particular classes of data analysis methods. The first chapters present both usual and multiway data analysis methods. Further chapters are dedicated for example to the analysis of spatial data, of phylogenetic structures, and of biodiversity patterns. One chapter deals with multivariate data analysis graphs.In each chapter, the basic mathematical definitions of the methods and the outputs of the R functions available in ade4 are detailed in two different boxes. The text of the book itself can be read independently from these boxes. Thus the book offers the opportunity to find information about the ecological situation from which a question raises alongside the mathematical properties of methods that can be applied to answer this question, as well as the details of software outputs. Each example and all the graphs in this book come with executable R code.

Multivariate Bayesian Statistics: Models for Source Separation and Signal Unmixing

Of the two primary approaches to the classic source separation problem, only one does not impose potentially unreasonable model and likelihood constraints: the Bayesian statistical approach. Bayesian methods incorporate the available information regarding the model parameters and not only allow estimation of the sources and mixing coefficients, but

Multivariate Calculus

This book is a compilation of all basic topics on functions of Several Variables and is primarily meant for undergraduate and post graduate students. Topics covered are: Limits, continuities and differentiabilities of functions of several variables. Properties of Implicit functions and Jacobians. Extreme values of multivariate functions. Various types of integrals in planes and surfaces and their related theorems including Dirichlet and Liouville’s extension to Dirichlet. Print edition not for sale in South Asia (India, Sri Lanka, Nepal, Bangladesh, Pakistan or Bhutan)

A Multivariate Claim Count Model for Applications in Insurance (Springer Actuarial)

This monograph presents a time-dynamic model for multivariate claim counts in actuarial applications. Inspired by real-world claim arrivals, the model balances interesting stylized facts (such as dependence across the components, over-dispersion and the clustering of claims) with a high level of mathematical tractability (including estimation, sampling and convergence results for large portfolios) and can thus be applied in various contexts (such as risk management and pricing of (re-)insurance contracts). The authors provide a detailed analysis of the proposed probabilistic model, discussing its relation to the existing literature, its statistical properties, different estimation strategies as well as possible applications and extensions. Actuaries and researchers working in risk management and premium pricing will find this book particularly interesting. Graduate-level probability theory, stochastic analysis and statistics are required.

Multivariate Data Analysis

Designed for the non-statistician, this applications-oriented introduction to multivariate analysis greatly reduces the amount of statistical notation and terminology used, while focusing instead on the fundamental concepts that affect the use of specific techniques. The fourth edition features an applicable six-step framework for each chapter, alongside revisited examples throughout. research design and data analysis courses taught in marketing, management and business departments.

Multivariate Data Integration Using R: Methods and Applications with the mixOmics Package (Chapman & Hall/CRC Computational Biology Series)

Large biological data, which are often noisy and high-dimensional, have become increasingly prevalent in biology and medicine. There is a real need for good training in statistics, from data exploration through to analysis and interpretation. This book provides an overview of statistical and dimension reduction methods for high-throughput biological data, with a specific focus on data integration. It starts with some biological background, key concepts underlying the multivariate methods, and then covers an array of methods implemented using the mixOmics package in R. Features: Provides a broad and accessible overview of methods for multi-omics data integration Covers a wide range of multivariate methods, each designed to answer specific biological questions Includes comprehensive visualisation techniques to aid in data interpretation Includes many worked examples and case studies using real data Includes reproducible R code for each multivariate method, using the mixOmics package The book is suitable for researchers from a wide range of scientific disciplines wishing to apply these methods to obtain new and deeper insights into biological mechanisms and biomedical problems. The suite of tools introduced in this book will enable students and scientists to work at the interface between, and provide critical collaborative expertise to, biologists, bioinformaticians, statisticians and clinicians.

Multivariate Density Estimation

Clarifies modern data analysis through nonparametric density estimation for a complete working knowledge of the theory and methods Featuring a thoroughly revised presentation, Multivariate Density Estimation: Theory, Practice, and Visualization, Second Edition maintains an intuitive approach to the underlying methodology and supporting theory of density estimation. Including new material and updated research in each chapter, the Second Edition presents additional clarification of theoretical opportunities, new algorithms, and up-to-date coverage of the unique challenges presented in the field of data analysis. The new edition focuses on the various density estimation techniques and methods that can be used in the field of big data. Defining optimal nonparametric estimators, the Second Edition demonstrates the density estimation tools to use when dealing with various multivariate structures in univariate, bivariate, trivariate, and quadrivariate data analysis. Continuing to illustrate the major concepts in the context of the classical histogram, Multivariate Density Estimation: Theory, Practice, and Visualization, Second Edition also features: Over 150 updated figures to clarify theoretical results and to show analyses of real data sets An updated presentation of graphic visualization using computer software such as R A clear discussion of selections of important research during the past decade, including mixture estimation, robust parametric modeling algorithms, and clustering More than 130 problems to help readers reinforce the main concepts and ideas presented Boxed theorems and results allowing easy identification of crucial ideas Multivariate Density Estimation: Theory, Practice, and Visualization, Second Edition is an ideal reference for theoretical and applied statisticians, practicing engineers, as well as readers interested in the theoretical aspects of nonparametric estimation and the application of these methods to multivariate data. The Second Edition is also useful as a textbook for introductory courses in kernel statistics, smoothing, advanced computational statistics, and general forms of statistical distributions.

Multivariate Discrete q-Distributions (Synthesis Lectures on Mathematics & Statistics)

This book is devoted to the study of multivariate discrete q-distributions, which is greatly facilitated by existing multivariate q-sequences and q-functions. Classical multivariate discrete distributions are defined on a sequence of independent and identically distributed Bernoulli trials, with either being a success of a certain rank (level) or a failure. The author relaxes the assumption that the probability of success of a trial is constant by assuming that it varies geometrically with the number of trials and/or the number of successes. The latter is advantageous in the sense that it permits incorporating the experience gained from the previous trials and/or successes, which leads to multivariate discrete q-distributions. Furthermore, q-multinomial and negative q-multinomial formulae are obtained. Next, the book addresses q-multinomial and negative q-multinomial distributions of the first and second kind. The author also examines multiple q-Polya urn model, multivariate q-Polya and inverse q-Polya distributions. Presents definitions and theorems that highlight key concepts and worked examples to illustrate the various applicationsContains numerous exercises at varying levels of difficulty that consolidate the presented concepts and resultsIncludes hints and answers to all exercises via the appendix and is supplemented with an Instructor's Solution Manual

Multivariate Exponential Families: A Concise Guide to Statistical Inference (SpringerBriefs in Statistics)

This book provides a concise introduction to exponential families. Parametric families of probability distributions and their properties are extensively studied in the literature on statistical modeling and inference. Exponential families of distributions comprise density functions of a particular form, which enables general assertions and leads to nice features. With a focus on parameter estimation and hypotheses testing, the text introduces the reader to distributional and statistical properties of multivariate and multiparameter exponential families along with a variety of detailed examples. The material is widely self-contained and written in a mathematical setting. It may serve both as a concise, mathematically rigorous course on exponential families in a systematic structure and as an introduction to Mathematical Statistics restricted to the use of exponential families.

Multivariate General Linear Models

Multivariate General Linear Models is an integrated introduction to multivariate multiple regression analysis (MMR) and multivariate analysis of variance (MANOVA). Beginning with an overview of the univariate general linear model, this volume defines the key steps in analyzing linear model data, and introduces multivariate linear model analysis as a generalization of the univariate model. The author focuses on multivariate measures of association for four common multivariate test statistics, presents a flexible method for testing hypotheses on models, and emphasizes the multivariate procedures attributable to Wilks, Pillai, Hotelling, and Roy. The volume concludes with a discussion of canonical correlation analysis that is shown to subsume all the multivariate procedures discussed in previous chapters. The analyses are illustrated throughout the text with three running examples drawing from several disciples, including personnel psychology, anthropology, environmental epidemiology, and neuropsychology.

Multivariate Humanities (Quantitative Methods in the Humanities and Social Sciences)

This case study-based textbook in multivariate analysis for advanced students in the humanities emphasizes descriptive, exploratory analyses of various types of data sets from a wide range of sub-disciplines, promoting the use of multivariate analysis and illustrating its wide applicability. Fields featured include, but are not limited to, historical agriculture, arts (music and painting), theology, and stylometrics (authorship issues). Most analyses are based on existing data, earlier analysed in published peer-reviewed papers.Four preliminary methodological and statistical chapters provide general technical background to the case studies. The multivariate statistical methods presented and illustrated include data inspection, several varieties of principal component analysis, correspondence analysis, multidimensional scaling, cluster analysis, regression analysis, discriminant analysis, and three-mode analysis.The bulk of the text is taken up by 14 case studies that lean heavily on graphical representations of statistical information such as biplots, using descriptive statistical techniques to support substantive conclusions. Each study features a description of the substantive background to the data, followed by discussion of appropriate multivariate techniques, and detailed results interpreted through graphical illustrations. Each study is concluded with a conceptual summary.

Multivariate Methods and Forecasting with IBM® SPSS® Statistics

This is the second of a two-part guide to quantitative analysis using the IBM SPSS Statistics software package; this volume focuses on multivariate statistical methods and advanced forecasting techniques. More often than not, regression models involve more than one independent variable. For example, forecasting methods are commonly applied to aggregates such as inflation rates, unemployment, exchange rates, etc. , that have complex relationships with determining variables. This book introduces multivariate regression models and provides examples to help understand theory underpinning the model. The book presents the fundamentals of multivariate regression and then moves on to examine several related techniques that have application in business-orientated fields such as logistic and multinomial regression. Forecasting tools such as the Box-Jenkins approach to time series modeling are introduced, as well as exponential smoothing and na#65533;ve techniques. This part also covers hot topics such as Factor Analysis, Discriminant Analysis and Multidimensional Scaling (MDS).

Multivariate Methods of Representing Relations in R for Prioritization Purposes

This monograph is multivariate, multi-perspective and multipurpose. We intend to be innovatively integrative through statistical synthesis. Innovation requires capacity to operate in ways that are not ordinary, which means that conventional computations and generic graphics will not meet the needs of an adaptive approach. Flexible formulation and special schematics are essential elements that must be manageable and economical.

Multivariate Modelling of Non-Stationary Economic Time Series

This book examines conventional time series in the context of stationary data prior to a discussion of cointegration, with a focus on multivariate models. The authors provide a detailed and extensive study of impulse responses and forecasting in the stationary and non-stationary context, considering small sample correction, volatility and the impact of different orders of integration. Models with expectations are considered along with alternate methods such as Singular Spectrum Analysis (SSA), the Kalman Filter and Structural Time Series, all in relation to cointegration. Using single equations methods to develop topics, and as examples of the notion of cointegration, Burke, Hunter, and Canepa provide direction and guidance to the now vast literature facing students and graduate economists.

Multivariate Nonparametric Regression and Visualization

A modern approach to statistical learning and its applications through visualization methodsWith a unique and innovative presentation, Multivariate Nonparametric Regression and Visualization provides readers with the core statistical concepts to obtain complete and accurate predictions when given a set of data. Focusing on nonparametric methods to adapt to the multiple types of data generatingmechanisms, the book begins with an overview of classification and regression.The book then introduces and examines various tested and proven visualization techniques for learning samples and functions. Multivariate Nonparametric Regression and Visualization identifies risk management, portfolio selection, and option pricing as the main areas in which statistical methods may be implemented in quantitative finance. The book provides coverage of key statistical areas including linear methods, kernel methods, additive models and trees, boosting, support vector machines, and nearest neighbor methods. Exploring the additional applications of nonparametric and semiparametric methods, Multivariate Nonparametric Regression and Visualization features:An extensive appendix with R-package training material to encourage duplication and modification of the presented computations and researchMultiple examples to demonstrate the applications in the field of financeSections with formal definitions of the various applied methods for readers to utilize throughout the bookMultivariate Nonparametric Regression and Visualization is an ideal textbook for upper-undergraduate and graduate-level courses on nonparametric function estimation, advanced topics in statistics, and quantitative finance. The book is also an excellent reference for practitioners who apply statistical methods in quantitative finance.

Multivariate Observations (Wiley Series in Probability and Statistics #547)

The Wiley-Interscience Paperback Series consists of selected books that have been made more accessible to consumers in an effort to increase global appeal and general circulation. With these new unabridged softcover volumes, Wiley hopes to extend the lives of these works by making them available to future generations of statisticians, mathematicians, and scientists. <p><p> "In recent years many monographs have been published on specialized aspects of multivariate data-analysis–on cluster analysis, multidimensional scaling, correspondence analysis, developments of discriminant analysis, graphical methods, classification, and so on. This book is an attempt to review these newer methods together with the classical theory. . . . This one merits two cheers." –J. C. Gower, Department of Statistics Rothamsted Experimental Station, Harpenden, U.K. Review in Biometrics, June 1987 <p><p> Multivariate Observations is a comprehensive sourcebook that treats data-oriented techniques as well as classical methods. Emphasis is on principles rather than mathematical detail, and coverage ranges from the practical problems of graphically representing high-dimensional data to the theoretical problems relating to matrices of random variables. Each chapter serves as a self-contained survey of a specific topic. The book includes many numerical examples and over 1,100 references.

Multivariate Statistical Analysis: A Conceptual Introduction

Multivariate Statistical Analysis in the Real and Complex Domains

This book explores topics in multivariate statistical analysis, relevant in the real and complex domains. It utilizes simplified and unified notations to render the complex subject matter both accessible and enjoyable, drawing from clear exposition and numerous illustrative examples. The book features an in-depth treatment of theory with a fair balance of applied coverage, and a classroom lecture style so that the learning process feels organic. It also contains original results, with the goal of driving research conversations forward.This will be particularly useful for researchers working in machine learning, biomedical signal processing, and other fields that increasingly rely on complex random variables to model complex-valued data. It can also be used in advanced courses on multivariate analysis. Numerous exercises are included throughout.

Multivariate Statistical Machine Learning Methods for Genomic Prediction

This book is open access under a CC BY 4.0 licenseThis open access book brings together the latest genome base prediction models currently being used by statisticians, breeders and data scientists. It provides an accessible way to understand the theory behind each statistical learning tool, the required pre-processing, the basics of model building, how to train statistical learning methods, the basic R scripts needed to implement each statistical learning tool, and the output of each tool. To do so, for each tool the book provides background theory, some elements of the R statistical software for its implementation, the conceptual underpinnings, and at least two illustrative examples with data from real-world genomic selection experiments. Lastly, worked-out examples help readers check their own comprehension.The book will greatly appeal to readers in plant (and animal) breeding, geneticists and statisticians, as it provides in a very accessible way the necessary theory, the appropriate R code, and illustrative examples for a complete understanding of each statistical learning tool. In addition, it weighs the advantages and disadvantages of each tool.

Multivariate Statistical Methods

MULTIVARIATE STATISTICAL METHODS fills a void in the marketplace, striking a crucial balance between the technical information and real-world applications of multivariate statistics. Donald Morrison has taught this course at the Wharton School for 33 years, and he has integrated his demonstrably successful teaching style into this textbook.

Multivariate Statistical Modeling in Engineering and Management

The book focuses on problem solving for practitioners and model building for academicians under multivariate situations. This book helps readers in understanding the issues, such as knowing variability, extracting patterns, building relationships, and making objective decisions. A large number of multivariate statistical models are covered in the book. The readers will learn how a practical problem can be converted to a statistical problem and how the statistical solution can be interpreted as a practical solution. Key features: • Links data generation process with statistical distributions in multivariate domain • Provides step by step procedure for estimating parameters of developed models • Provides blueprint for data driven decision making • Includes practical examples and case studies relevant for intended audiences The book will help everyone involved in data driven problem solving, modeling and decision making.

Multivariate Statistical Quality Control Using R

The intensive use of automatic data acquisition system and the use of cloud computing for process monitoring have led to an increased occurrence of industrial processes that utilize statistical process control and capability analysis. These analyses are performed almost exclusively with multivariate methodologies. The aim of this Brief is to present the most important MSQC techniques developed in R language. The book is divided into two parts. The first part contains the basic R elements, an introduction to statistical procedures, and the main aspects related to Statistical Quality Control (SQC). The second part covers the construction of multivariate control charts, the calculation of Multivariate Capability Indices.

Multivariate Statistics

The authors present tools and concepts of multivariate data analysis by means of exercises and their solutions. The first part is devoted to graphical techniques. The second part deals with multivariate random variables and presents the derivation of estimators and tests for various practical situations. The last part introduces a wide variety of exercises in applied multivariate data analysis. The book demonstrates the application of simple calculus and basic multivariate methods in real life situations. It contains altogether more than 250 solved exercises which can assist a university teacher in setting up a modern multivariate analysis course. All computer-based exercises are available in the R language. All data sets are included in the library SMSdata that may be downloaded via the quantlet download center www. quantlet. org. Data sets are available also via the Springer webpage. For interactive display of low-dimensional projections of a multivariate data set, we recommend GGobi.

Multivariate Statistics Made Simple: A Practical Approach

This book explains the advanced but essential concepts of Multivariate Statistics in a practical way while touching the mathematical logic in a befitting manner. The illustrations are based on real case studies from a super specialty hospital where active research is going on.