Clustering With Finite Data From Semi Parametric Mixture Distributions
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Mixture Models
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Author : Weixin Yao
language : en
Publisher: CRC Press
Release Date : 2024-04-18
Mixture Models written by Weixin Yao and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-04-18 with Mathematics categories.
Mixture models are a powerful tool for analyzing complex and heterogeneous datasets across many scientific fields, from finance to genomics. Mixture Models: Parametric, Semiparametric, and New Directions provides an up-to-date introduction to these models, their recent developments, and their implementation using R. It fills a gap in the literature by covering not only the basics of finite mixture models, but also recent developments such as semiparametric extensions, robust modeling, label switching, and high-dimensional modeling. Features Comprehensive overview of the methods and applications of mixture models Key topics include hypothesis testing, model selection, estimation methods, and Bayesian approaches Recent developments, such as semiparametric extensions, robust modeling, label switching, and high-dimensional modeling Examples and case studies from such fields as astronomy, biology, genomics, economics, finance, medicine, engineering, and sociology Integrated R code for many of the models, with code and data available in the R Package MixSemiRob Mixture Models: Parametric, Semiparametric, and New Directions is a valuable resource for researchers and postgraduate students from statistics, biostatistics, and other fields. It could be used as a textbook for a course on model-based clustering methods, and as a supplementary text for courses on data mining, semiparametric modeling, and high-dimensional data analysis.
Finite Mixture Models
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Author : Geoffrey McLachlan
language : en
Publisher:
Release Date : 2019
Finite Mixture Models written by Geoffrey McLachlan and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with categories.
The important role of finite mixture models in the statistical analysis of data is underscored by the ever-increasing rate at which articles on mixture applications appear in the statistical and general scientific literature. The aim of this article is to provide an up-to-date account of the theory and methodological developments underlying the applications of finite mixture models. Because of their flexibility, mixture models are being increasingly exploited as a convenient, semiparametric way in which to model unknown distributional shapes. This is in addition to their obvious applications where there is group-structure in the data or where the aim is to explore the data for such structure, as in a cluster analysis. It has now been three decades since the publication of the monograph by McLachlan & Basford (1988) with an emphasis on the potential usefulness of mixture models for inference and clustering. Since then, mixture models have attracted the interest of many researchers and have found many new and interesting fields of application. Thus, the literature on mixture models has expanded enormously, and as a consequence, the bibliography here can only provide selected coverage.
Finite Mixture Models
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Author : Geoffrey McLachlan
language : en
Publisher: John Wiley & Sons
Release Date : 2004-03-22
Finite Mixture Models written by Geoffrey McLachlan and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-03-22 with Mathematics categories.
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.
Handbook Of Mixture Analysis
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Author : Sylvia Fruhwirth-Schnatter
language : en
Publisher: CRC Press
Release Date : 2019-01-04
Handbook Of Mixture Analysis written by Sylvia Fruhwirth-Schnatter and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-01-04 with Computers categories.
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.
Model Based Clustering Classification And Density Estimation Using Mclust In R
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Author : Luca Scrucca
language : en
Publisher: CRC Press
Release Date : 2023-04-20
Model Based Clustering Classification And Density Estimation Using Mclust In R written by Luca Scrucca and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-04-20 with Mathematics categories.
Model-Based Clustering, Classification, and Denisty Estimation Using mclust in R Model-based clustering and classification methods provide a systematic statistical approach to clustering, classification, and density estimation via mixture modeling. The model-based framework allows the problems of choosing or developing an appropriate clustering or classification method to be understood within the context of statistical modeling. The mclust package for the statistical environment R is a widely adopted platform implementing these model-based strategies. The package includes both summary and visual functionality, complementing procedures for estimating and choosing models. Key features of the book: An introduction to the model-based approach and the mclust R package A detailed description of mclust and the underlying modeling strategies An extensive set of examples, color plots, and figures along with the R code for reproducing them Supported by a companion website, including the R code to reproduce the examples and figures presented in the book, errata, and other supplementary material Model-Based Clustering, Classification, and Density Estimation Using mclust in R is accessible to quantitatively trained students and researchers with a basic understanding of statistical methods, including inference and computing. In addition to serving as a reference manual for mclust, the book will be particularly useful to those wishing to employ these model-based techniques in research or applications in statistics, data science, clinical research, social science, and many other disciplines.
Statistical Analysis Of Finite Mixture Distributions
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Author : D. M. Titterington
language : en
Publisher:
Release Date : 1985
Statistical Analysis Of Finite Mixture Distributions written by D. M. Titterington and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985 with Mathematics categories.
In this book, the authors give a complete account of the applications, mathematical structure and statistical analysis of finite mixture distributions.
Finite Mixture Distributions
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Author : B. Everitt
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-08
Finite Mixture Distributions written by B. Everitt and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-08 with Science categories.
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.
Handbook Of Cluster Analysis
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Author : Christian Hennig
language : en
Publisher: CRC Press
Release Date : 2015-12-16
Handbook Of Cluster Analysis written by Christian Hennig and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-12-16 with Business & Economics categories.
Handbook of Cluster Analysis provides a comprehensive and unified account of the main research developments in cluster analysis. Written by active, distinguished researchers in this area, the book helps readers make informed choices of the most suitable clustering approach for their problem and make better use of existing cluster analysis tools.The
Bayesian Non And Semi Parametric Methods And Applications
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Author : Peter Rossi
language : en
Publisher: Princeton University Press
Release Date : 2014-04-27
Bayesian Non And Semi Parametric Methods And Applications written by Peter Rossi and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-04-27 with Business & Economics categories.
This book reviews and develops Bayesian non-parametric and semi-parametric methods for applications in microeconometrics and quantitative marketing. Most econometric models used in microeconomics and marketing applications involve arbitrary distributional assumptions. As more data becomes available, a natural desire to provide methods that relax these assumptions arises. Peter Rossi advocates a Bayesian approach in which specific distributional assumptions are replaced with more flexible distributions based on mixtures of normals. The Bayesian approach can use either a large but fixed number of normal components in the mixture or an infinite number bounded only by the sample size. By using flexible distributional approximations instead of fixed parametric models, the Bayesian approach can reap the advantages of an efficient method that models all of the structure in the data while retaining desirable smoothing properties. Non-Bayesian non-parametric methods often require additional ad hoc rules to avoid "overfitting," in which resulting density approximates are nonsmooth. With proper priors, the Bayesian approach largely avoids overfitting, while retaining flexibility. This book provides methods for assessing informative priors that require only simple data normalizations. The book also applies the mixture of the normals approximation method to a number of important models in microeconometrics and marketing, including the non-parametric and semi-parametric regression models, instrumental variables problems, and models of heterogeneity. In addition, the author has written a free online software package in R, "bayesm," which implements all of the non-parametric models discussed in the book.
Partitional Clustering Algorithms
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Author : M. Emre Celebi
language : en
Publisher: Springer
Release Date : 2014-11-07
Partitional Clustering Algorithms written by M. Emre Celebi and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-11-07 with Technology & Engineering categories.
This book focuses on partitional clustering algorithms, which are commonly used in engineering and computer scientific applications. The goal of this volume is to summarize the state-of-the-art in partitional clustering. The book includes such topics as center-based clustering, competitive learning clustering and density-based clustering. Each chapter is contributed by a leading expert in the field.