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Nonlinear Mixture Models

Author: Tatiana Tatarinova
Publisher: World Scientific
ISBN: 1783266279
Size: 48.23 MB
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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. Contents:IntroductionMathematical Description of Nonlinear Mixture ModelsLabel Switching and TrappingTreatment of Mixture Models with an Unknown Number of ComponentsApplications of BDMCMC, KLMCMC, and RPSNonparametric MethodsBayesian Clustering Methods Readership: Graduate students and researchers in bioinformatics, mathematical biology, probability and statistics, mathematical modeling, and pharmacokinetics. Keywords:Nonlinear Mixture Models;Bayesian Analysis;Monte Carlo Markov Chain

Finite Mixture And Markov Switching Models

Author: Sylvia Frühwirth-Schnatter
Publisher: Springer Science & Business Media
ISBN: 0387357688
Size: 32.54 MB
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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.

Finite Mixture Models

Author: Geoffrey McLachlan
Publisher: John Wiley & Sons
ISBN: 047165406X
Size: 13.78 MB
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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.

Handbook Of Blind Source Separation

Author: Pierre Comon
Publisher: Academic Press
ISBN: 9780080884943
Size: 41.77 MB
Format: PDF
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Edited by the people who were forerunners in creating the field, together with contributions from 34 leading international experts, this handbook provides the definitive reference on Blind Source Separation, giving a broad and comprehensive description of all the core principles and methods, numerical algorithms and major applications in the fields of telecommunications, biomedical engineering and audio, acoustic and speech processing. Going beyond a machine learning perspective, the book reflects recent results in signal processing and numerical analysis, and includes topics such as optimization criteria, mathematical tools, the design of numerical algorithms, convolutive mixtures, and time frequency approaches. This Handbook is an ideal reference for university researchers, R&D engineers and graduates wishing to learn the core principles, methods, algorithms, and applications of Blind Source Separation. Covers the principles and major techniques and methods in one book Edited by the pioneers in the field with contributions from 34 of the world’s experts Describes the main existing numerical algorithms and gives practical advice on their design Covers the latest cutting edge topics: second order methods; algebraic identification of under-determined mixtures, time-frequency methods, Bayesian approaches, blind identification under non negativity approaches, semi-blind methods for communications Shows the applications of the methods to key application areas such as telecommunications, biomedical engineering, speech, acoustic, audio and music processing, while also giving a general method for developing applications

Mixtures

Author: Kerrie L. Mengersen
Publisher: John Wiley & Sons
ISBN: 1119998441
Size: 79.38 MB
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This book uses the EM (expectation maximization) algorithm tosimultaneously estimate the missing data and unknown parameter(s)associated with a data set. The parameters describe the componentdistributions of the mixture; the distributions may be continuousor discrete. The editors provide a complete account of the applications,mathematical structure and statistical analysis of finite mixturedistributions along with MCMC computational methods, together witha range of detailed discussions covering the applications of themethods and features chapters from the leading experts on thesubject. 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, andits methodology attracts interest from researchers in the fields inwhich it can be applied.

Applied Bayesian Hierarchical Methods

Author: Peter D. Congdon
Publisher: CRC Press
ISBN: 9781584887218
Size: 33.91 MB
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The use of Markov chain Monte Carlo (MCMC) methods for estimating hierarchical models involves complex data structures and is often described as a revolutionary development. An intermediate-level treatment of Bayesian hierarchical models and their applications, Applied Bayesian Hierarchical Methods demonstrates the advantages of a Bayesian approach to data sets involving inferences for collections of related units or variables and in methods where parameters can be treated as random collections. Emphasizing computational issues, the book provides examples of the following application settings: meta-analysis, data structured in space or time, multilevel and longitudinal data, multivariate data, nonlinear regression, and survival time data. For the worked examples, the text mainly employs the WinBUGS package, allowing readers to explore alternative likelihood assumptions, regression structures, and assumptions on prior densities. It also incorporates BayesX code, which is particularly useful in nonlinear regression. To demonstrate MCMC sampling from first principles, the author includes worked examples using the R package. Through illustrative data analysis and attention to statistical computing, this book focuses on the practical implementation of Bayesian hierarchical methods. It also discusses several issues that arise when applying Bayesian techniques in hierarchical and random effects models.

Bayesian Methods For Nonlinear Classification And Regression

Author: David G. T. Denison
Publisher: John Wiley & Sons
ISBN: 9780471490364
Size: 12.84 MB
Format: PDF, ePub, Docs
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Regression analysis models the relationship between a set of responses and another variable. But data rarely conforms to simple curves and straight lines - parametric models - and this text examines more complex - or nonparametric - models.

Finite Mixture Models

Author: Geoffrey McLachlan
Publisher: John Wiley & Sons
ISBN: 047165406X
Size: 62.84 MB
Format: PDF, Mobi
View: 611
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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.

Nonlinear Dynamics Volume 2

Author: Gaetan Kerschen
Publisher: Springer Science & Business Media
ISBN: 3319045229
Size: 62.47 MB
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This second volume of eight from the IMAC - XXXII Conference, brings together contributions to this important area of research and engineering. The collection presents early findings and case studies on fundamental and applied aspects of Structural Dynamics, including papers on: Linear Systems Substructure Modelling Adaptive Structures Experimental Techniques Analytical Methods Damage Detection Damping of Materials & Members Modal Parameter Identification Modal Testing Methods System Identification Active Control Modal Parameter Estimation Processing Modal Data

Structural Equation Modeling

Author: Sik-Yum Lee
Publisher: John Wiley & Sons
ISBN: 0470024240
Size: 24.87 MB
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***Winner of the 2008 Ziegel Prize for outstanding new book of the year*** Structural equation modeling (SEM) is a powerful multivariate method allowing the evaluation of a series of simultaneous hypotheses about the impacts of latent and manifest variables on other variables, taking measurement errors into account. As SEMs have grown in popularity in recent years, new models and statistical methods have been developed for more accurate analysis of more complex data. A Bayesian approach to SEMs allows the use of prior information resulting in improved parameter estimates, latent variable estimates, and statistics for model comparison, as well as offering more reliable results for smaller samples. Structural Equation Modeling introduces the Bayesian approach to SEMs, including the selection of prior distributions and data augmentation, and offers an overview of the subject’s recent advances. Demonstrates how to utilize powerful statistical computing tools, including the Gibbs sampler, the Metropolis-Hasting algorithm, bridge sampling and path sampling to obtain the Bayesian results. Discusses the Bayes factor and Deviance Information Criterion (DIC) for model comparison. Includes coverage of complex models, including SEMs with ordered categorical variables, and dichotomous variables, nonlinear SEMs, two-level SEMs, multisample SEMs, mixtures of SEMs, SEMs with missing data, SEMs with variables from an exponential family of distributions, and some of their combinations. Illustrates the methodology through simulation studies and examples with real data from business management, education, psychology, public health and sociology. Demonstrates the application of the freely available software WinBUGS via a supplementary website featuring computer code and data sets. Structural Equation Modeling: A Bayesian Approach is a multi-disciplinary text ideal for researchers and students in many areas, including: statistics, biostatistics, business, education, medicine, psychology, public health and social science.