Finite Mixture Models

Author : Geoffrey McLachlan,David Peel
Publisher : John Wiley & Sons
Page : 419 pages
File Size : 41,8 Mb
Release : 2004-03-22
Category : Mathematics
ISBN : 9780471654063

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Finite Mixture Models by Geoffrey McLachlan,David Peel Pdf

An up-to-date, comprehensive account of major issues in finitemixture modeling This volume provides an up-to-date account of the theory andapplications of modeling via finite mixture distributions. With anemphasis on the applications of mixture models in both mainstreamanalysis and other areas such as unsupervised pattern recognition,speech recognition, and medical imaging, the book describes theformulations of the finite mixture approach, details itsmethodology, discusses aspects of its implementation, andillustrates its application in many common statisticalcontexts. Major issues discussed in this book include identifiabilityproblems, actual fitting of finite mixtures through use of the EMalgorithm, properties of the maximum likelihood estimators soobtained, assessment of the number of components to be used in themixture, and the applicability of asymptotic theory in providing abasis for the solutions to some of these problems. The author alsoconsiders how the EM algorithm can be scaled to handle the fittingof mixture models to very large databases, as in data miningapplications. This comprehensive, practical guide: * Provides more than 800 references-40% published since 1995 * Includes an appendix listing available mixture software * Links statistical literature with machine learning and patternrecognition literature * Contains more than 100 helpful graphs, charts, and tables Finite Mixture Models is an important resource for both applied andtheoretical statisticians as well as for researchers in the manyareas in which finite mixture models can be used to analyze data.

Author : Geoffrey J. McLachlan,David Peel
Publisher : John Wiley & Sons
Page : 468 pages
File Size : 44,5 Mb
Release : 2000-10-02
Category : Mathematics
ISBN : 9780471006268

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Finite Mixture Models by Geoffrey J. McLachlan,David Peel Pdf

An up-to-date, comprehensive account of major issues in finite mixture modeling This volume provides an up-to-date account of the theory and applications of modeling via finite mixture distributions. With an emphasis on the applications of mixture models in both mainstream analysis and other areas such as unsupervised pattern recognition, speech recognition, and medical imaging, the book describes the formulations of the finite mixture approach, details its methodology, discusses aspects of its implementation, and illustrates its application in many common statistical contexts. Major issues discussed in this book include identifiability problems, actual fitting of finite mixtures through use of the EM algorithm, properties of the maximum likelihood estimators so obtained, assessment of the number of components to be used in the mixture, and the applicability of asymptotic theory in providing a basis for the solutions to some of these problems. The author also considers how the EM algorithm can be scaled to handle the fitting of mixture models to very large databases, as in data mining applications. This comprehensive, practical guide: * Provides more than 800 references-40% published since 1995 * Includes an appendix listing available mixture software * Links statistical literature with machine learning and pattern recognition literature * Contains more than 100 helpful graphs, charts, and tables Finite Mixture Models is an important resource for both applied and theoretical statisticians as well as for researchers in the many areas in which finite mixture models can be used to analyze data.

Author : Geoffrey J. McLachlan,David Peel
Publisher : John Wiley & Sons
Page : 468 pages
File Size : 50,7 Mb
Release : 2000-10-02
Category : Mathematics
ISBN : 9780471006268

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Finite Mixture Models by Geoffrey J. McLachlan,David Peel Pdf

An up-to-date, comprehensive account of major issues in finite mixture modeling This volume provides an up-to-date account of the theory and applications of modeling via finite mixture distributions. With an emphasis on the applications of mixture models in both mainstream analysis and other areas such as unsupervised pattern recognition, speech recognition, and medical imaging, the book describes the formulations of the finite mixture approach, details its methodology, discusses aspects of its implementation, and illustrates its application in many common statistical contexts. Major issues discussed in this book include identifiability problems, actual fitting of finite mixtures through use of the EM algorithm, properties of the maximum likelihood estimators so obtained, assessment of the number of components to be used in the mixture, and the applicability of asymptotic theory in providing a basis for the solutions to some of these problems. The author also considers how the EM algorithm can be scaled to handle the fitting of mixture models to very large databases, as in data mining applications. This comprehensive, practical guide: * Provides more than 800 references-40% published since 1995 * Includes an appendix listing available mixture software * Links statistical literature with machine learning and pattern recognition literature * Contains more than 100 helpful graphs, charts, and tables Finite Mixture Models is an important resource for both applied and theoretical statisticians as well as for researchers in the many areas in which finite mixture models can be used to analyze data.

Author : Sylvia Frühwirth-Schnatter
Publisher : Springer Science & Business Media
Page : 506 pages
File Size : 53,8 Mb
Release : 2006-11-24
Category : Mathematics
ISBN : 9780387357683

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Finite Mixture and Markov Switching Models by Sylvia Frühwirth-Schnatter Pdf

The past decade has seen powerful new computational tools for modeling which combine a Bayesian approach with recent Monte simulation techniques based on Markov chains. This book is the first to offer a systematic presentation of the Bayesian perspective of finite mixture modelling. The book is designed to show finite mixture and Markov switching models are formulated, what structures they imply on the data, their potential uses, and how they are estimated. Presenting its concepts informally without sacrificing mathematical correctness, it will serve a wide readership including statisticians as well as biologists, economists, engineers, financial and market researchers.

Author : Nizar Bouguila,Wentao Fan
Publisher : Springer
Page : 355 pages
File Size : 52,6 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.

Author : Peter Schlattmann
Publisher : Springer Science & Business Media
Page : 252 pages
File Size : 45,9 Mb
Release : 2009-03-02
Category : Medical
ISBN : 9783540686514

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Medical Applications of Finite Mixture Models by Peter Schlattmann Pdf

Patients are not alike! This simple truth is often ignored in the analysis of me- cal data, since most of the time results are presented for the “average” patient. As a result, potential variability between patients is ignored when presenting, e.g., the results of a multiple linear regression model. In medicine there are more and more attempts to individualize therapy; thus, from the author’s point of view biostatis- cians should support these efforts. Therefore, one of the tasks of the statistician is to identify heterogeneity of patients and, if possible, to explain part of it with known explanatory covariates. Finite mixture models may be used to aid this purpose. This book tries to show that there are a large range of applications. They include the analysis of gene - pression data, pharmacokinetics, toxicology, and the determinants of beta-carotene plasma levels. Other examples include disease clustering, data from psychophysi- ogy, and meta-analysis of published studies. The book is intended as a resource for those interested in applying these methods.

Author : B. Everitt
Publisher : Springer Science & Business Media
Page : 148 pages
File Size : 50,7 Mb
Release : 2013-03-08
Category : Science
ISBN : 9789400958975

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Finite Mixture Distributions by B. Everitt Pdf

Finite mixture distributions arise in a variety of applications ranging from the length distribution of fish to the content of DNA in the nuclei of liver cells. The literature surrounding them is large and goes back to the end of the last century when Karl Pearson published his well-known paper on estimating the five parameters in a mixture of two normal distributions. In this text we attempt to review this literature and in addition indicate the practical details of fitting such distributions to sample data. Our hope is that the monograph will be useful to statisticians interested in mixture distributions and to re search workers in other areas applying such distributions to their data. We would like to express our gratitude to Mrs Bertha Lakey for typing the manuscript. Institute oj Psychiatry B. S. Everitt University of London D. l Hand 1980 CHAPTER I General introduction 1. 1 Introduction This monograph is concerned with statistical distributions which can be expressed as superpositions of (usually simpler) component distributions. Such superpositions are termed mixture distributions or compound distributions. For example, the distribution of height in a population of children might be expressed as follows: h(height) = fg(height: age)f(age)d age (1. 1) where g(height: age) is the conditional distribution of height on age, and/(age) is the age distribution of the children in the population.

Author : Christian Homburg,Martin Klarmann,Arnd Vomberg
Publisher : Springer
Page : 0 pages
File Size : 42,9 Mb
Release : 2021-12-03
Category : Business & Economics
ISBN : 3319574116

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Handbook of Market Research by Christian Homburg,Martin Klarmann,Arnd Vomberg Pdf

In this handbook, internationally renowned scholars outline the current state-of-the-art of quantitative and qualitative market research. They discuss focal approaches to market research and guide students and practitioners in their real-life applications. Aspects covered include topics on data-related issues, methods, and applications. Data-related topics comprise chapters on experimental design, survey research methods, international market research, panel data fusion, and endogeneity. Method-oriented chapters look at a wide variety of data analysis methods relevant for market research, including chapters on regression, structural equation modeling (SEM), conjoint analysis, and text analysis. Application chapters focus on specific topics relevant for market research such as customer satisfaction, customer retention modeling, return on marketing, and return on price promotions. Each chapter is written by an expert in the field. The presentation of the material seeks to improve the intuitive and technical understanding of the methods covered.

Author : Paul D. McNicholas
Publisher : CRC Press
Page : 212 pages
File Size : 53,5 Mb
Release : 2016-10-04
Category : Mathematics
ISBN : 9781482225679

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Mixture Model-Based Classification by Paul D. McNicholas Pdf

"This is a great overview of the field of model-based clustering and classification by one of its leading developers. McNicholas provides a resource that I am certain will be used by researchers in statistics and related disciplines for quite some time. The discussion of mixtures with heavy tails and asymmetric distributions will place this text as the authoritative, modern reference in the mixture modeling literature." (Douglas Steinley, University of Missouri) Mixture Model-Based Classification is the first monograph devoted to mixture model-based approaches to clustering and classification. This is both a book for established researchers and newcomers to the field. A history of mixture models as a tool for classification is provided and Gaussian mixtures are considered extensively, including mixtures of factor analyzers and other approaches for high-dimensional data. Non-Gaussian mixtures are considered, from mixtures with components that parameterize skewness and/or concentration, right up to mixtures of multiple scaled distributions. Several other important topics are considered, including mixture approaches for clustering and classification of longitudinal data as well as discussion about how to define a cluster Paul D. McNicholas is the Canada Research Chair in Computational Statistics at McMaster University, where he is a Professor in the Department of Mathematics and Statistics. His research focuses on the use of mixture model-based approaches for classification, with particular attention to clustering applications, and he has published extensively within the field. He is an associate editor for several journals and has served as a guest editor for a number of special issues on mixture models.

Author : Sylvia Fruhwirth-Schnatter,Gilles Celeux,Christian P. Robert
Publisher : CRC Press
Page : 388 pages
File Size : 46,7 Mb
Release : 2019-01-04
Category : Computers
ISBN : 9780429508868

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Handbook of Mixture Analysis by Sylvia Fruhwirth-Schnatter,Gilles Celeux,Christian P. Robert Pdf

Mixture models have been around for over 150 years, and they are found in many branches of statistical modelling, as a versatile and multifaceted tool. They can be applied to a wide range of data: univariate or multivariate, continuous or categorical, cross-sectional, time series, networks, and much more. Mixture analysis is a very active research topic in statistics and machine learning, with new developments in methodology and applications taking place all the time. The Handbook of Mixture Analysis is a very timely publication, presenting a broad overview of the methods and applications of this important field of research. It covers a wide array of topics, including the EM algorithm, Bayesian mixture models, model-based clustering, high-dimensional data, hidden Markov models, and applications in finance, genomics, and astronomy. Features: Provides a comprehensive overview of the methods and applications of mixture modelling and analysis Divided into three parts: Foundations and Methods; Mixture Modelling and Extensions; and Selected Applications Contains many worked examples using real data, together with computational implementation, to illustrate the methods described Includes contributions from the leading researchers in the field The Handbook of Mixture Analysis is targeted at graduate students and young researchers new to the field. It will also be an important reference for anyone working in this field, whether they are developing new methodology, or applying the models to real scientific problems.

Author : Todd D. Little
Publisher : Unknown
Page : 785 pages
File Size : 48,9 Mb
Release : 2013-03-21
Category : Psychology
ISBN : 9780199934898

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The Oxford Handbook of Quantitative Methods in Psychology: Vol. 2 by Todd D. Little Pdf

The Oxford Handbook of Quantitative Methods in Psychology provides an accessible and comprehensive review of the current state-of-the-science and a one-stop source for learning and reviewing current best-practices in a quantitative methods across the social, behavioral, and educational sciences.

Author : Bruce G. Lindsay
Publisher : IMS
Page : 184 pages
File Size : 44,7 Mb
Release : 1995
Category : Mathematics
ISBN : 0940600323

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Mixture Models by Bruce G. Lindsay Pdf

Author : Kerrie L. Mengersen,Christian Robert,Mike Titterington
Publisher : John Wiley & Sons
Page : 357 pages
File Size : 43,6 Mb
Release : 2011-05-03
Category : Mathematics
ISBN : 9781119998440

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Mixtures by Kerrie L. Mengersen,Christian Robert,Mike Titterington Pdf

This book uses the EM (expectation maximization) algorithm to simultaneously estimate the missing data and unknown parameter(s) associated with a data set. The parameters describe the component distributions of the mixture; the distributions may be continuous or discrete. The editors provide a complete account of the applications, mathematical structure and statistical analysis of finite mixture distributions along with MCMC computational methods, together with a range of detailed discussions covering the applications of the methods and features chapters from the leading experts on the subject. The applications are drawn from scientific discipline, including biostatistics, computer science, ecology and finance. This area of statistics is important to a range of disciplines, and its methodology attracts interest from researchers in the fields in which it can be applied.

Author : Shu-Kay Ng
Publisher : CRC Press
Page : 222 pages
File Size : 42,7 Mb
Release : 2019-05-03
Category : Mathematics
ISBN : 9780429529092

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Mixture Modelling for Medical and Health Sciences by Shu-Kay Ng Pdf

Mixture Modelling for Medical and Health Sciences provides a direct connection between theoretical developments in mixture modelling and their applications in real world problems. The book describes the development of the most important concepts through comprehensive analyses of real and practical examples taken from real-life research problems in

Author : Charles Bouveyron,Gilles Celeux,T. Brendan Murphy,Adrian E. Raftery
Publisher : Cambridge University Press
Page : 446 pages
File Size : 51,9 Mb
Release : 2019-07-25
Category : Business & Economics
ISBN : 9781108494205

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Model-Based Clustering and Classification for Data Science by Charles Bouveyron,Gilles Celeux,T. Brendan Murphy,Adrian E. Raftery Pdf

Colorful example-rich introduction to the state-of-the-art for students in data science, as well as researchers and practitioners.