Mixture Model-Based Classification

Mixture Model-Based

"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 Computation...

  • ASIN: 1482225662

Finite Mixture Models

Finite Mixture

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 literatu...

  • ASIN: 0471006262

Nonlinear Mixture Models: A Bayesian Approach

Nonlinear Mixture Models: A Bayesian

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 componen...

  • ASIN: 1848167563

Finite Mixture and Markov Switching Models (Springer Series in Statistics)

Finite Mixture and Markov Switching Models (Springer Series

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.

  • ASIN: 0387329099

Growth Modeling: Structural Equation and Multilevel Modeling Approaches (Methodology in the Social Sciences)

Growth Modeling: Structural Equation and Multilevel Modeling Approaches

Growth models are among the core methods for analyzing how and when people change. Discussing both structural equation and multilevel modeling approaches, this book leads readers step by step through applying each model to longitudinal data to answer particular research questions. It demonstrates cutting-edge ways to describe linear and nonlinear change patterns, examine within-person and between-person differences in change, study change in latent variables, identify leading and lagging indicators of change, evaluate co-occurring patterns of change across multiple variables, and more. User-friendly features include real data examples, code (for Mplus or NLMIXED in SAS, and OpenMx or nlme in R), discussion of the output, and interpretation of each model's results. User-Friendly Features *Real, worked-through longitudinal data examples serving as illustrations in each chapter. *Script boxes that provide code for fitting the models to example data and facilitate application to the reader's own data. *"Important Considerations" sections offering caveats, warnings, and recommendations for the use of specific models. *Companion website supplying datasets and syntax for the book's examples, along with additional code in SAS/R for linear mixed-effects modeling.

  • ASIN: 1462526063

Biased Sampling, Over-identified Parameter Problems and Beyond (ICSA Book Series in Statistics)

Biased Sampling, Over-identified Parameter Problems and Beyond (ICSA

This book is devoted to biased sampling problems (also called choice-based sampling in Econometrics parlance) and over-identified parameter estimation problems. Biased sampling problems appear in many areas of research, including Medicine, Epidemiology and Public Health, the Social Sciences and Economics. The book addresses a range of important topics, including case and control studies, causal inference, missing data problems, meta-analysis, renewal process and length biased sampling problems, capture and recapture problems, case cohort studies, exponential tilting genetic mixture models etc.The goal of this book is to make it easier for Ph. D students and new researchers to get started in this research area. It will be of interest to all those who work in the health, biological, social and physical sciences, as well as those who are interested in survey methodology and other areas of statistical science, among others. 

  • ASIN: 9811048541

Advances in Latent Variable Mixture Models (NA)

Advances in Latent Variable Mixture Models

The current volume, Advances in Latent Variable Mixture Models, contains chapters by all of the speakers who participated in the 2006 CILVR conference, providing not just a snapshot of the event, but more importantly chronicling the state of the art in latent variable mixture model research. The volume starts with an overview chapter by the CILVR conference keynote speaker, Bengt Muthén, offering a "lay of the land"for latent variable mixture models before the volume moves to more specific constellations of topics. Part I, Multilevel and Longitudinal Systems, deals with mixtures for data that are hierarchical in nature either due to the data's sampling structure or to the repetition of measures (of varied types) over time. Part II, Models for Assessment and Diagnosis, addresses scenarios for making judgments about individuals' state of knowledge or development, and about the instruments used for making such judgments. Finally, Part III, Challenges in Model Evaluation, focuses on some of the methodological issues associated with the selection of models most accurately representing the processes and populations under investigation. It should be stated that this volume is not intended to be a first exposure to latent variable methods. Readers lacking such foundational knowledge a...

  • Brand: Brand: Information Age Publishing
  • ASIN: 1593118473

Testing Lack of Fit in a Mixture Model

Testing Lack of Fit in a Mixture

Abstract:A common problem in modeling the response surface in most systems, and in particular in a mixture system, is that of detecting lack of fit, or inadequancy, of a fitted model of the form E(Y) = Xg, in comparison to a model of the form E{Y) = Xe,+ X B postulated as the true model. One method for detecting lack of fit involves comparing the value of the response observed at certain locations in the factor space, called "check points," with the value of the response that the fitted model predicts at these same check points.The observations at the check points are used only for testing lack of fit and are not used in fitting the model.It is shown that under the usual assumptions of independent and normally distributed errors, the lack of fit test statistic which uses the data at the check points is an F statistic. When no lack of fit is present the statistic possesses a central F distribution, but in general, in the presence of lack of fit, the statistic possesses a doubly noncentral F distribution. The power of this F test depends on the location of the check points in the factor space through its noncentrality parameters. A method of selecting check points that maximize the power of the test for lack of fit through their influence on the numerator noncentrality parameter is...

  • ASIN: 0530006685

Handbook of Mixture Analysis (Chapman & Hall/CRC Handbooks of Modern Statistical Methods)

Handbook of Mixture Analysis (Chapman & Hall/CRC Handbooks

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 Analysi...

  • ASIN: 1498763812

Higher-Order Growth Curves and Mixture Modeling with Mplus (Multivariate Applications Series)

Higher-Order Growth Curves and Mixture Modeling with Mplus

This practical introduction to second-order and growth mixture models using Mplus introduces simple and complex techniques through incremental steps. The authors extend latent growth curves to second-order growth curve and mixture models and then combine the two. To maximize understanding, each model is presented with basic structural equations, figures with associated syntax that highlight what the statistics mean, Mplus applications, and an interpretation of results. Examples from a variety of disciplines demonstrate the use of the models and exercises allow readers to test their understanding of the techniques. A comprehensive introduction to confirmatory factor analysis, latent growth curve modeling, and growth mixture modeling is provided so the book can be used by readers of various skill levels. The book’s datasets are available on the web. Highlights include: -Illustrative examples using Mplus 7.4 include conceptual figures, Mplus program syntax, and an interpretation of results to show readers how to carry out the analyses with actual data. -Exercises with an answer key allow readers to practice the skills they learn. -Applications to a variety of disciplines appeal to those in the behavioral, social, political, educational, occupational, business, and health sciences....

  • Brand: imusti
  • ASIN: 1138925152
Similar Mixture Models Results
Mixture Models Video Results
           

(ML 16.6) Gaussian mixture model (Mixture of Gaussians)

Mixture Models

Introduction to the mixture of Gaussians, a.k.a. Gaussian mixture model (GMM). This is often used for density estimation and clustering.

Tags: machine learning,statistics,math

Gaussian Mixture Models - The Math of Intelligence (Week 7)

Mixture Models

We're going to predict customer churn using a clustering technique called the Gaussian Mixture Model! This is a probability distribution that consists of multiple Gaussian distributions, very cool. I also have something important but unrelated to say in the beginning of the video. Code for this ...

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EM algorithm: how it works

Mixture Models

Full lecture: http://bit.ly/EM-alg Mixture models are a probabilistically-sound way to do soft clustering. We assume our data is sampled from K different sources (probability distributions). The expectation maximisation (EM) algorithm allows us to discover the parameters of these distributions, ...

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