The Statistical Analysis Of Compositional Data

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Applied Compositional Data Analysis

Peter Filzmoser,Karel Hron,Matthias Templ
Applied Compositional Data Analysis Book PDF

Author : Peter Filzmoser,Karel Hron,Matthias Templ
Publisher : Springer
Page : 280 pages
File Size : 50,6 Mb
Release : 2018-11-03
Category : Mathematics
ISBN : 9783319964225

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Applied Compositional Data Analysis by Peter Filzmoser,Karel Hron,Matthias Templ Pdf

This book presents the statistical analysis of compositional data using the log-ratio approach. It includes a wide range of classical and robust statistical methods adapted for compositional data analysis, such as supervised and unsupervised methods like PCA, correlation analysis, classification and regression. In addition, it considers special data structures like high-dimensional compositions and compositional tables. The methodology introduced is also frequently compared to methods which ignore the specific nature of compositional data. It focuses on practical aspects of compositional data analysis rather than on detailed theoretical derivations, thus issues like graphical visualization and preprocessing (treatment of missing values, zeros, outliers and similar artifacts) form an important part of the book. Since it is primarily intended for researchers and students from applied fields like geochemistry, chemometrics, biology and natural sciences, economics, and social sciences, all the proposed methods are accompanied by worked-out examples in R using the package robCompositions.

The Statistical Analysis of Compositional Data

J. Aitchison
The Statistical Analysis of Compositional Data Book PDF

Author : J. Aitchison
Publisher : Springer
Page : 440 pages
File Size : 52,6 Mb
Release : 1986-08-21
Category : Science
ISBN : UCAL:B4407249

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The Statistical Analysis of Compositional Data by J. Aitchison Pdf

As long ago as 1897 Karl Pearson, in a now classic paper on spurious correlation, first pointed out dangers that may befall the analyst who attempts to interpret correlations between ratios whose numerators and denominators contain common parts. He thus implied that the analysis of compositional data, with its concentration on relation ships between proportions of some whole, is likely to be fraught with difficulty. History has proved him correct: over the succeeding years and indeed right up to the present day, there has been no other form of data analysis where more confusion has reigned and where more improper and inadequate statistical methods have been applied. The special and intrinsic feature of compositional data is that the proportions of a composition are naturally subject to a unit-sum constraint. For other forms of constrained data, in particular for directional data where there is a unit-length constraint on each direction vector, scientist and statistician alike have readily appre ciated that new statistical methods, appropriate to the special nature of the data, are required; and there now exists an extensive literature on the successful statistical analysis of directional data. It is paradox ical that for compositional data, subject to an apparently simpler constraint, such an appreciation and development have been slower to emerge. In applications the unit-sum constraint has been widely ignored or wished away and inappropriate 'standard' statistical methods, devised for and successfully applied to unconstrained data, have been used with disastrous consequences.

Compositional Data Analysis

Vera Pawlowsky-Glahn,Antonella Buccianti
Compositional Data Analysis Book PDF

Author : Vera Pawlowsky-Glahn,Antonella Buccianti
Publisher : John Wiley & Sons
Page : 401 pages
File Size : 48,7 Mb
Release : 2011-09-19
Category : Mathematics
ISBN : 9780470711354

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Compositional Data Analysis by Vera Pawlowsky-Glahn,Antonella Buccianti Pdf

It is difficult to imagine that the statistical analysis of compositional data has been a major issue of concern for more than 100 years. It is even more difficult to realize that so many statisticians and users of statistics are unaware of the particular problems affecting compositional data, as well as their solutions. The issue of ``spurious correlation'', as the situation was phrased by Karl Pearson back in 1897, affects all data that measures parts of some whole, such as percentages, proportions, ppm and ppb. Such measurements are present in all fields of science, ranging from geology, biology, environmental sciences, forensic sciences, medicine and hydrology. This book presents the history and development of compositional data analysis along with Aitchison's log-ratio approach. Compositional Data Analysis describes the state of the art both in theoretical fields as well as applications in the different fields of science. Key Features: Reflects the state-of-the-art in compositional data analysis. Gives an overview of the historical development of compositional data analysis, as well as basic concepts and procedures. Looks at advances in algebra and calculus on the simplex. Presents applications in different fields of science, including, genomics, ecology, biology, geochemistry, planetology, chemistry and economics. Explores connections to correspondence analysis and the Dirichlet distribution. Presents a summary of three available software packages for compositional data analysis. Supported by an accompanying website featuring R code. Applied scientists working on compositional data analysis in any field of science, both in academia and professionals will benefit from this book, along with graduate students in any field of science working with compositional data.

Compositional Data Analysis in the Geosciences

Antonella Buccianti,G. Mateu-Figueras,Vera Pawlowsky-Glahn
Compositional Data Analysis in the Geosciences Book PDF

Author : Antonella Buccianti,G. Mateu-Figueras,Vera Pawlowsky-Glahn
Publisher : Geological Society of London
Page : 232 pages
File Size : 49,8 Mb
Release : 2006
Category : Mathematics
ISBN : 1862392056

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Compositional Data Analysis in the Geosciences by Antonella Buccianti,G. Mateu-Figueras,Vera Pawlowsky-Glahn Pdf

Since Karl Pearson wrote his paper on spurious correlation in 1897, a lot has been said about the statistical analysis of compositional data, mainly by geologists such as Felix Chayes. The solution appeared in the 1980s, when John Aitchison proposed to use Iogratios. Since then, the approach has seen a great expansion, mainly building on the idea of the `natural geometry' of the sample space. Statistics is expected to give sense to our perception of the natural scale of the data, and this is made possible for compositional data using Iogratios. This publication will be a milestone in this process.

Modeling and Analysis of Compositional Data

Vera Pawlowsky-Glahn,Juan José Egozcue,Raimon Tolosana-Delgado
Modeling and Analysis of Compositional Data Book PDF

Author : Vera Pawlowsky-Glahn,Juan José Egozcue,Raimon Tolosana-Delgado
Publisher : John Wiley & Sons
Page : 272 pages
File Size : 47,7 Mb
Release : 2015-02-17
Category : Mathematics
ISBN : 9781119003137

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Modeling and Analysis of Compositional Data by Vera Pawlowsky-Glahn,Juan José Egozcue,Raimon Tolosana-Delgado Pdf

Modeling and Analysis of Compositional Data presents a practical and comprehensive introduction to the analysis of compositional data along with numerous examples to illustrate both theory and application of each method. Based upon short courses delivered by the authors, it provides a complete and current compendium of fundamental to advanced methodologies along with exercises at the end of each chapter to improve understanding, as well as data and a solutions manual which is available on an accompanying website. Complementing Pawlowsky-Glahn’s earlier collective text that provides an overview of the state-of-the-art in this field, Modeling and Analysis of Compositional Data fills a gap in the literature for a much-needed manual for teaching, self learning or consulting.

Analyzing Compositional Data with R

K. Gerald van den Boogaart,Raimon Tolosana-Delgado
Analyzing Compositional Data with R Book PDF

Author : K. Gerald van den Boogaart,Raimon Tolosana-Delgado
Publisher : Springer Science & Business Media
Page : 269 pages
File Size : 45,6 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9783642368097

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Analyzing Compositional Data with R by K. Gerald van den Boogaart,Raimon Tolosana-Delgado Pdf

This book presents the statistical analysis of compositional data sets, i.e., data in percentages, proportions, concentrations, etc. The subject is covered from its grounding principles to the practical use in descriptive exploratory analysis, robust linear models and advanced multivariate statistical methods, including zeros and missing values, and paying special attention to data visualization and model display issues. Many illustrated examples and code chunks guide the reader into their modeling and interpretation. And, though the book primarily serves as a reference guide for the R package “compositions,” it is also a general introductory text on Compositional Data Analysis. Awareness of their special characteristics spread in the Geosciences in the early sixties, but a strategy for properly dealing with them was not available until the works of Aitchison in the eighties. Since then, research has expanded our understanding of their theoretical principles and the potentials and limitations of their interpretation. This is the first comprehensive textbook addressing these issues, as well as their practical implications with regard to software. The book is intended for scientists interested in statistically analyzing their compositional data. The subject enjoys relatively broad awareness in the geosciences and environmental sciences, but the spectrum of recent applications also covers areas like medicine, official statistics, and economics. Readers should be familiar with basic univariate and multivariate statistics. Knowledge of R is recommended but not required, as the book is self-contained.

Modeling and Analysis of Compositional Data

Vera Pawlowsky-Glahn,Juan José Egozcue,Raimon Tolosana-Delgado
Modeling and Analysis of Compositional Data Book PDF

Author : Vera Pawlowsky-Glahn,Juan José Egozcue,Raimon Tolosana-Delgado
Publisher : John Wiley & Sons
Page : 273 pages
File Size : 51,6 Mb
Release : 2015-03-30
Category : Mathematics
ISBN : 9781118443064

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Modeling and Analysis of Compositional Data by Vera Pawlowsky-Glahn,Juan José Egozcue,Raimon Tolosana-Delgado Pdf

Modeling and Analysis of Compositional Data presents a practical and comprehensive introduction to the analysis of compositional data along with numerous examples to illustrate both theory and application of each method. Based upon short courses delivered by the authors, it provides a complete and current compendium of fundamental to advanced methodologies along with exercises at the end of each chapter to improve understanding, as well as data and a solutions manual which is available on an accompanying website. Complementing Pawlowsky-Glahn’s earlier collective text that provides an overview of the state-of-the-art in this field, Modeling and Analysis of Compositional Data fills a gap in the literature for a much-needed manual for teaching, self learning or consulting.

Compositional Data Analysis in Practice

Michael Greenacre
Compositional Data Analysis in Practice Book PDF

Author : Michael Greenacre
Publisher : CRC Press
Page : 120 pages
File Size : 48,8 Mb
Release : 2018-07-17
Category : Business & Economics
ISBN : 9780429849015

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Compositional Data Analysis in Practice by Michael Greenacre Pdf

Compositional Data Analysis in Practice is a user-oriented practical guide to the analysis of data with the property of a constant sum, for example percentages adding up to 100%. Compositional data can give misleading results if regular statistical methods are applied, and are best analysed by first transforming them to logarithms of ratios. This book explains how this transformation affects the analysis, results and interpretation of this very special type of data. All aspects of compositional data analysis are considered: visualization, modelling, dimension-reduction, clustering and variable selection, with many examples in the fields of food science, archaeology, sociology and biochemistry, and a final chapter containing a complete case study using fatty acid compositions in ecology. The applicability of these methods extends to other fields such as linguistics, geochemistry, marketing, economics and finance. R Software The R package easyCODA, which accompanies this book, can be downloaded from R-Forge as follows: install.packages("easyCODA", repos="") and will be available on CRAN soon. Notice that the R packages ca and vegan also have to be installed (from CRAN in the usual way).

Bayesian Forecasting and Dynamic Models

Mike West,Jeff Harrison
Bayesian Forecasting and Dynamic Models Book PDF

Author : Mike West,Jeff Harrison
Publisher : Springer Science & Business Media
Page : 720 pages
File Size : 48,6 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9781475793659

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Bayesian Forecasting and Dynamic Models by Mike West,Jeff Harrison Pdf

In this book we are concerned with Bayesian learning and forecast ing in dynamic environments. We describe the structure and theory of classes of dynamic models, and their uses in Bayesian forecasting. The principles, models and methods of Bayesian forecasting have been developed extensively during the last twenty years. This devel opment has involved thorough investigation of mathematical and sta tistical aspects of forecasting models and related techniques. With this has come experience with application in a variety of areas in commercial and industrial, scientific and socio-economic fields. In deed much of the technical development has been driven by the needs of forecasting practitioners. As a result, there now exists a relatively complete statistical and mathematical framework, although much of this is either not properly documented or not easily accessible. Our primary goals in writing this book have been to present our view of this approach to modelling and forecasting, and to provide a rea sonably complete text for advanced university students and research workers. The text is primarily intended for advanced undergraduate and postgraduate students in statistics and mathematics. In line with this objective we present thorough discussion of mathematical and statistical features of Bayesian analyses of dynamic models, with illustrations, examples and exercises in each Chapter.

Compositional Data Analysis

Josep Antoni Martín-Fernández,Santiago Thió-Henestrosa
Compositional Data Analysis Book PDF

Author : Josep Antoni Martín-Fernández,Santiago Thió-Henestrosa
Publisher : Springer
Page : 209 pages
File Size : 50,8 Mb
Release : 2016-11-19
Category : Mathematics
ISBN : 9783319448114

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Compositional Data Analysis by Josep Antoni Martín-Fernández,Santiago Thió-Henestrosa Pdf

The authoritative contributions gathered in this volume reflect the state of the art in compositional data analysis (CoDa). The respective chapters cover all aspects of CoDa, ranging from mathematical theory, statistical methods and techniques to its broad range of applications in geochemistry, the life sciences and other disciplines. The selected and peer-reviewed papers were originally presented at the 6th International Workshop on Compositional Data Analysis, CoDaWork 2015, held in L’Escala (Girona), Spain. Compositional data is defined as vectors of positive components and constant sum, and, more generally, all those vectors representing parts of a whole which only carry relative information. Examples of compositional data can be found in many different fields such as geology, chemistry, economics, medicine, ecology and sociology. As most of the classical statistical techniques are incoherent on compositions, in the 1980s John Aitchison proposed the log-ratio approach to CoDa. This became the foundation of modern CoDa, which is now based on a specific geometric structure for the simplex, an appropriate representation of the sample space of compositional data. The International Workshops on Compositional Data Analysis offer a vital discussion forum for researchers and practitioners concerned with the statistical treatment and modelling of compositional data or other constrained data sets and the interpretation of models and their applications. The goal of the workshops is to summarize and share recent developments, and to identify important lines of future research.

Geostatistical Analysis of Compositional Data

Vera Pawlowsky-Glahn,Ricardo A. Olea
Geostatistical Analysis of Compositional Data Book PDF

Author : Vera Pawlowsky-Glahn,Ricardo A. Olea
Publisher : Oxford University Press
Page : 204 pages
File Size : 51,9 Mb
Release : 2004-06-03
Category : Business & Economics
ISBN : 9780195171662

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Geostatistical Analysis of Compositional Data by Vera Pawlowsky-Glahn,Ricardo A. Olea Pdf

1. Introduction. 2. Regionalized Compositions. 3. Spatial Covariance Structure. 4. Concepts of Null Correlation. 5. Cokriging. 6. Practical Aspects of Compositional Data Analysis. 7. Application to Real Data. Summary and Prospects. References. Index.

Mixture Models and Applications

Nizar Bouguila,Wentao Fan
Mixture Models and Applications Book PDF

Author : Nizar Bouguila,Wentao Fan
Publisher : Springer
Page : 355 pages
File Size : 53,8 Mb
Release : 2019-08-13
Category : Technology & Engineering
ISBN : 9783030238766

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Mixture Models and Applications by Nizar Bouguila,Wentao Fan Pdf

This book focuses on recent advances, approaches, theories and applications related to mixture models. In particular, it presents recent unsupervised and semi-supervised frameworks that consider mixture models as their main tool. The chapters considers mixture models involving several interesting and challenging problems such as parameters estimation, model selection, feature selection, etc. The goal of this book is to summarize the recent advances and modern approaches related to these problems. Each contributor presents novel research, a practical study, or novel applications based on mixture models, or a survey of the literature. Reports advances on classic problems in mixture modeling such as parameter estimation, model selection, and feature selection; Present theoretical and practical developments in mixture-based modeling and their importance in different applications; Discusses perspectives and challenging future works related to mixture modeling.

Geostatistics for Compositional Data with R

Raimon Tolosana-Delgado,Ute Mueller
Geostatistics for Compositional Data with R Book PDF

Author : Raimon Tolosana-Delgado,Ute Mueller
Publisher : Springer Nature
Page : 275 pages
File Size : 45,5 Mb
Release : 2021-11-19
Category : Mathematics
ISBN : 9783030825683

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Geostatistics for Compositional Data with R by Raimon Tolosana-Delgado,Ute Mueller Pdf

This book provides a guided approach to the geostatistical modelling of compositional spatial data. These data are data in proportions, percentages or concentrations distributed in space which exhibit spatial correlation. The book can be divided into four blocks. The first block sets the framework and provides some background on compositional data analysis. Block two introduces compositional exploratory tools for both non-spatial and spatial aspects. Block three covers all necessary facets of multivariate spatial prediction for compositional data: variogram modelling, cokriging and validation. Finally, block four details strategies for simulation of compositional data, including transformations to multivariate normality, Gaussian cosimulation, multipoint simulation of compositional data, and common postprocessing techniques, valid for both Gaussian and multipoint methods. All methods are illustrated via applications to two types of data sets: one a large-scale geochemical survey, comprised of a full suite of geochemical variables, and the other from a mining context, where only the elements of greatest importance are considered. R codes are included for all aspects of the methodology, encapsulated in the R package "gmGeostats", available in CRAN.

Geostatistical Functional Data Analysis

Jorge Mateu,Ramon Giraldo
Geostatistical Functional Data Analysis Book PDF

Author : Jorge Mateu,Ramon Giraldo
Publisher : John Wiley & Sons
Page : 452 pages
File Size : 50,5 Mb
Release : 2021-12-13
Category : Social Science
ISBN : 9781119387848

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Geostatistical Functional Data Analysis by Jorge Mateu,Ramon Giraldo Pdf

Geostatistical Functional Data Analysis Explore the intersection between geostatistics and functional data analysis with this insightful new reference Geostatistical Functional Data Analysis presents a unified approach to modelling functional data when spatial and spatio-temporal correlations are present. The Editors link together the wide research areas of geostatistics and functional data analysis to provide the reader with a new area called geostatistical functional data analysis that will bring new insights and new open questions to researchers coming from both scientific fields. This book provides a complete and up-to-date account to deal with functional data that is spatially correlated, but also includes the most innovative developments in different open avenues in this field. Containing contributions from leading experts in the field, this practical guide provides readers with the necessary tools to employ and adapt classic statistical techniques to handle spatial regression. The book also includes: A thorough introduction to the spatial kriging methodology when working with functions A detailed exposition of more classical statistical techniques adapted to the functional case and extended to handle spatial correlations Practical discussions of ANOVA, regression, and clustering methods to explore spatial correlation in a collection of curves sampled in a region In-depth explorations of the similarities and differences between spatio-temporal data analysis and functional data analysis Aimed at mathematicians, statisticians, postgraduate students, and researchers involved in the analysis of functional and spatial data, Geostatistical Functional Data Analysis will also prove to be a powerful addition to the libraries of geoscientists, environmental scientists, and economists seeking insightful new knowledge and questions at the interface of geostatistics and functional data analysis.

Advances in Compositional Data Analysis

Peter Filzmoser,Karel Hron,Josep Antoni Martín-Fernández,Javier Palarea-Albaladejo
Advances in Compositional Data Analysis Book PDF

Author : Peter Filzmoser,Karel Hron,Josep Antoni Martín-Fernández,Javier Palarea-Albaladejo
Publisher : Springer Nature
Page : 404 pages
File Size : 47,5 Mb
Release : 2021-06-01
Category : Mathematics
ISBN : 9783030711757

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Advances in Compositional Data Analysis by Peter Filzmoser,Karel Hron,Josep Antoni Martín-Fernández,Javier Palarea-Albaladejo Pdf

This book presents modern methods and real-world applications of compositional data analysis. It covers a wide variety of topics, ranging from an updated presentation of basic concepts and ideas in compositional data analysis to recent advances in the context of complex data structures. Further, it illustrates real-world applications in numerous scientific disciplines and includes references to the latest software solutions available for compositional data analysis, thus providing a valuable and up-to-date guide for researchers and practitioners working with compositional data. Featuring selected contributions by leading experts in the field, the book is dedicated to Vera Pawlowsky-Glahn on the occasion of her 70th birthday.