Finite Mixture Distributions

Author : B. Everitt
Publisher : Springer Science & Business Media
Page : 148 pages
File Size : 51,6 Mb
Release : 2013-03-08
Category : Science
ISBN : 9789400958975

Get Book

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 : D. M. Titterington,A. F. M. Smith,Adrian F. M. Smith,U. E. Makov
Publisher : Unknown
Page : 264 pages
File Size : 40,8 Mb
Release : 1985
Category : Mathematics
ISBN : UCSD:31822002319770

Get Book

Statistical Analysis of Finite Mixture Distributions by D. M. Titterington,A. F. M. Smith,Adrian F. M. Smith,U. E. Makov Pdf

In this book, the authors give a complete account of the applications, mathematical structure and statistical analysis of finite mixture distributions.

Author : Geoffrey McLachlan,David Peel
Publisher : John Wiley & Sons
Page : 419 pages
File Size : 40,5 Mb
Release : 2004-03-22
Category : Mathematics
ISBN : 9780471654063

Get Book

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 : Nizar Bouguila,Wentao Fan
Publisher : Springer
Page : 355 pages
File Size : 49,6 Mb
Release : 2019-08-13
Category : Technology & Engineering
ISBN : 9783030238766

Get Book

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 : Sylvia Frühwirth-Schnatter
Publisher : Springer Science & Business Media
Page : 506 pages
File Size : 44,8 Mb
Release : 2006-11-24
Category : Mathematics
ISBN : 9780387357683

Get Book

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 : Víctor Hugo Lachos Dávila,Celso Rômulo Barbosa Cabral,Camila Borelli Zeller
Publisher : Springer
Page : 101 pages
File Size : 53,6 Mb
Release : 2018-11-12
Category : Mathematics
ISBN : 9783319980294

Get Book

Finite Mixture of Skewed Distributions by Víctor Hugo Lachos Dávila,Celso Rômulo Barbosa Cabral,Camila Borelli Zeller Pdf

This book presents recent results in finite mixtures of skewed distributions to prepare readers to undertake mixture models using scale mixtures of skew normal distributions (SMSN). For this purpose, the authors consider maximum likelihood estimation for univariate and multivariate finite mixtures where components are members of the flexible class of SMSN distributions. This subclass includes the entire family of normal independent distributions, also known as scale mixtures of normal distributions (SMN), as well as the skew-normal and skewed versions of some other classical symmetric distributions: the skew-t (ST), the skew-slash (SSL) and the skew-contaminated normal (SCN), for example. These distributions have heavier tails than the typical normal one, and thus they seem to be a reasonable choice for robust inference. The proposed EM-type algorithm and methods are implemented in the R package mixsmsn, highlighting the applicability of the techniques presented in the book. This work is a useful reference guide for researchers analyzing heterogeneous data, as well as a textbook for a graduate-level course in mixture models. The tools presented in the book make complex techniques accessible to applied researchers without the advanced mathematical background and will have broad applications in fields like medicine, biology, engineering, economic, geology and chemistry.

Author : Abram van Dijk
Publisher : Rozenberg Publishers
Page : 138 pages
File Size : 48,6 Mb
Release : 2009
Category : Electronic
ISBN : 9789036101349

Get Book

Essays on finite mixture models by Abram van Dijk Pdf

Finite mixture distributions are a weighted average of a finite number of distributions. The latter are usually called the mixture components. The weights are usually described by a multinomial distribution and are sometimes called mixing proportions. The mixture components may be the same type of distributions with di®erent parameter values but they may also be completely different distributions. Therefore, finite mixture distributions are very °exible for modeling data. They are frequently used as a building block within many modern econometric models. The specification of the mixture distribution depends on the modeling problem at hand. In this thesis, we introduce new applications of finite mixtures to deal with several di®erent modeling issues. Each chapter of the thesis focusses on a specific modeling issue. The parameters of some of the resulting models can be estimated using standard techniques but for some of the chapters we need to develop new estimation and inference methods. To illustrate how the methods can be applied, we analyze at least one empirical data set for each approach. These data sets cover a wide range of research fields, such as macroeconomics, marketing, and political science. We show the usefulness of the methods and, in some cases, the improvement over previous methods in the literature.

Author : Sylvia Fruhwirth-Schnatter,Gilles Celeux,Christian P. Robert
Publisher : CRC Press
Page : 388 pages
File Size : 47,7 Mb
Release : 2019-01-04
Category : Computers
ISBN : 9780429508868

Get Book

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 : Bruce G. Lindsay
Publisher : IMS
Page : 184 pages
File Size : 52,8 Mb
Release : 1995
Category : Mathematics
ISBN : 0940600323

Get Book

Mixture Models by Bruce G. Lindsay Pdf

Author : Kerrie L. Mengersen,Christian Robert,Mike Titterington
Publisher : John Wiley & Sons
Page : 357 pages
File Size : 40,9 Mb
Release : 2011-05-03
Category : Mathematics
ISBN : 9781119998440

Get Book

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 : A K Gupta,D K Nagar
Publisher : CRC Press
Page : 151 pages
File Size : 51,7 Mb
Release : 2018-05-02
Category : Mathematics
ISBN : 9781351433006

Get Book

Matrix Variate Distributions by A K Gupta,D K Nagar Pdf

Useful in physics, economics, psychology, and other fields, random matrices play an important role in the study of multivariate statistical methods. Until now, however, most of the material on random matrices could only be found scattered in various statistical journals. Matrix Variate Distributions gathers and systematically presents most of the recent developments in continuous matrix variate distribution theory and includes new results. After a review of the essential background material, the authors investigate the range of matrix variate distributions, including: matrix variate normal distribution Wishart distribution Matrix variate t-distribution Matrix variate beta distribution F-distribution Matrix variate Dirichlet distribution Matrix quadratic forms With its inclusion of new results, Matrix Variate Distributions promises to stimulate further research and help advance the field of multivariate statistical analysis.

Author : Paul D. McNicholas
Publisher : CRC Press
Page : 212 pages
File Size : 52,9 Mb
Release : 2016-10-04
Category : Mathematics
ISBN : 9781482225679

Get Book

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 : Christian Homburg,Martin Klarmann,Arnd Vomberg
Publisher : Springer
Page : 0 pages
File Size : 48,6 Mb
Release : 2021-12-03
Category : Business & Economics
ISBN : 3319574116

Get Book

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 : Kees van Montfort,Johan Oud,Albert Satorra
Publisher : Routledge
Page : 464 pages
File Size : 54,5 Mb
Release : 2017-09-29
Category : Education
ISBN : 9781351559751

Get Book

Longitudinal Models in the Behavioral and Related Sciences by Kees van Montfort,Johan Oud,Albert Satorra Pdf

This volume reviews longitudinal models and analysis procedures for use in the behavioral and social sciences. Written by distinguished experts in the field, the book presents the most current approaches and theories, and the technical problems that may be encountered along the way. Readers will find new ideas about the use of longitudinal analysis in solving problems that arise due to the specific nature of the research design and the data available. Longitudinal Models in the Behavioral and Related Sciences opens with the latest theoretical developments. In particular, the book addresses situations that arise due to the categorical nature of the data, issues related to state space modeling, and potential problems that may arise from network analysis and/or growth-curve data. The focus of part two is on the application of longitudinal modeling in a variety of disciplines. The book features applications such as heterogeneity on the patterns of a firm’s profit, on house prices, and on delinquent behavior; non-linearity in growth in assessing cognitive aging; measurement error issues in longitudinal research; and distance association for the analysis of change. Part two clearly demonstrates the caution that should be taken when applying longitudinal modeling as well as in the interpretation of the results. This new volume is ideal for advanced students and researchers in psychology, sociology, education, economics, management, medicine, and neuroscience.

Author : Shalabh,Christian Heumann
Publisher : Springer Science & Business Media
Page : 448 pages
File Size : 54,8 Mb
Release : 2008-07-11
Category : Mathematics
ISBN : 9783790820645

Get Book

Recent Advances in Linear Models and Related Areas by Shalabh,Christian Heumann Pdf

This collection contains invited papers by distinguished statisticians to honour and acknowledge the contributions of Professor Dr. Dr. Helge Toutenburg to Statistics on the occasion of his sixty-?fth birthday. These papers present the most recent developments in the area of the linear model and its related topics. Helge Toutenburg is an established statistician and currently a Professor in the Department of Statistics at the University of Munich (Germany) and Guest Professor at the University of Basel (Switzerland). He studied Mathematics in his early years at Berlin and specialized in Statistics. Later he completed his dissertation (Dr. rer. nat. ) in 1969 on optimal prediction procedures at the University of Berlin and completed the post-doctoral thesis in 1989 at the University of Dortmund on the topic of mean squared error superiority. He taught at the Universities of Berlin, Dortmund and Regensburg before joining the University of Munich in 1991. He has various areas of interest in which he has authored and co-authored over 130 research articles and 17 books. He has made pioneering contributions in several areas of statistics, including linear inference, linear models, regression analysis, quality engineering, Taguchi methods, analysis of variance, design of experiments, and statistics in medicine and dentistry.