Mixture Models and Applications

Mixture Models and Applications
Author: Nizar Bouguila
Publisher: Springer
Total Pages: 356
Release: 2019-08-13
Genre: Technology & Engineering
ISBN: 3030238768

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.

Finite Mixture Models

Finite Mixture Models
Author: Geoffrey McLachlan
Publisher: John Wiley & Sons
Total Pages: 419
Release: 2004-03-22
Genre: Mathematics
ISBN: 047165406X

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.

Mixture Models

Mixture Models
Author: Bruce G. Lindsay
Publisher: IMS
Total Pages: 184
Release: 1995
Genre: Mathematics
ISBN: 9780940600324

Encyclopedia of Biometrics

Encyclopedia of Biometrics
Author: Stan Z. Li
Publisher: Springer Science & Business Media
Total Pages: 1466
Release: 2009-08-27
Genre: Computers
ISBN: 0387730028

With an A–Z format, this encyclopedia provides easy access to relevant information on all aspects of biometrics. It features approximately 250 overview entries and 800 definitional entries. Each entry includes a definition, key words, list of synonyms, list of related entries, illustration(s), applications, and a bibliography. Most entries include useful literature references providing the reader with a portal to more detailed information.

Medical Applications of Finite Mixture Models

Medical Applications of Finite Mixture Models
Author: Peter Schlattmann
Publisher: Springer Science & Business Media
Total Pages: 252
Release: 2009-03-02
Genre: Medical
ISBN: 3540686517

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.

Finite Mixture and Markov Switching Models

Finite Mixture and Markov Switching Models
Author: Sylvia Frühwirth-Schnatter
Publisher: Springer Science & Business Media
Total Pages: 506
Release: 2006-11-24
Genre: Mathematics
ISBN: 0387357688

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.

Nonlinear Mixture Models: A Bayesian Approach

Nonlinear Mixture Models: A Bayesian Approach
Author: Tatiana V Tatarinova
Publisher: World Scientific
Total Pages: 296
Release: 2014-12-30
Genre: Mathematics
ISBN: 1783266279

This book, written by two mathematicians from the University of Southern California, provides a broad introduction to the important subject of nonlinear mixture models from a Bayesian perspective. It contains background material, a brief description of Markov chain theory, as well as novel algorithms and their applications. It is self-contained and unified in presentation, which makes it ideal for use as an advanced textbook by graduate students and as a reference for independent researchers. The explanations in the book are detailed enough to capture the interest of the curious reader, and complete enough to provide the necessary background material needed to go further into the subject and explore the research literature.In this book the authors present Bayesian methods of analysis for nonlinear, hierarchical mixture models, with a finite, but possibly unknown, number of components. These methods are then applied to various problems including population pharmacokinetics and gene expression analysis. In population pharmacokinetics, the nonlinear mixture model, based on previous clinical data, becomes the prior distribution for individual therapy. For gene expression data, one application included in the book is to determine which genes should be associated with the same component of the mixture (also known as a clustering problem). The book also contains examples of computer programs written in BUGS. This is the first book of its kind to cover many of the topics in this field.

Mixture Model-Based Classification

Mixture Model-Based Classification
Author: Paul D. McNicholas
Publisher: CRC Press
Total Pages: 212
Release: 2016-10-04
Genre: Mathematics
ISBN: 1482225670

"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.

Mixture Models

Mixture Models
Author: Weixin Yao
Publisher: CRC Press
Total Pages: 398
Release: 2024-04-18
Genre: Mathematics
ISBN: 1040009875

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.

Statistical Inference Under Mixture Models

Statistical Inference Under Mixture Models
Author: Jiahua Chen
Publisher: Springer Nature
Total Pages: 330
Release: 2023-12-24
Genre: Mathematics
ISBN: 9819961416

This book puts its weight on theoretical issues related to finite mixture models. It shows that a good applicant, is an applicant who understands the issues behind each statistical method. This book is intended for applicants whose interests include some understanding of the procedures they are using, while they do not have to read the technical derivations. At the same time, many researchers find most theories and techniques necessary for the development of various statistical methods, without chasing after one set of research papers, after another. Even though the book emphasizes the theory, it provides accessible numerical tools for data analysis. Readers with strength in developing statistical software, may find it useful.