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Author: Tatiana V Tatarinova Publisher: World Scientific ISBN: 1783266279 Category : Mathematics Languages : en Pages : 296
Book Description
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.
Author: Tatiana V Tatarinova Publisher: World Scientific ISBN: 1783266279 Category : Mathematics Languages : en Pages : 296
Book Description
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.
Author: Marie Davidian Publisher: Routledge ISBN: 1351428144 Category : Mathematics Languages : en Pages : 380
Book Description
Nonlinear measurement data arise in a wide variety of biological and biomedical applications, such as longitudinal clinical trials, studies of drug kinetics and growth, and the analysis of assay and laboratory data. Nonlinear Models for Repeated Measurement Data provides the first unified development of methods and models for data of this type, with a detailed treatment of inference for the nonlinear mixed effects and its extensions. A particular strength of the book is the inclusion of several detailed case studies from the areas of population pharmacokinetics and pharmacodynamics, immunoassay and bioassay development and the analysis of growth curves.
Author: Marie Davidian Publisher: Routledge ISBN: 1351428152 Category : Mathematics Languages : en Pages : 360
Book Description
Nonlinear measurement data arise in a wide variety of biological and biomedical applications, such as longitudinal clinical trials, studies of drug kinetics and growth, and the analysis of assay and laboratory data. Nonlinear Models for Repeated Measurement Data provides the first unified development of methods and models for data of this type, with a detailed treatment of inference for the nonlinear mixed effects and its extensions. A particular strength of the book is the inclusion of several detailed case studies from the areas of population pharmacokinetics and pharmacodynamics, immunoassay and bioassay development and the analysis of growth curves.
Author: David G. T. Denison Publisher: John Wiley & Sons ISBN: 9780471490364 Category : Mathematics Languages : en Pages : 302
Book Description
Bei der Regressionsanalyse von Datenmaterial erhält man leider selten lineare oder andere einfache Zusammenhänge (parametrische Modelle). Dieses Buch hilft Ihnen, auch komplexere, nichtparametrische Modelle zu verstehen und zu beherrschen. Stärken und Schwächen jedes einzelnen Modells werden durch die Anwendung auf Standarddatensätze demonstriert. Verbreitete nichtparametrische Modelle werden mit Hilfe von Bayes-Verfahren in einen kohärenten wahrscheinlichkeitstheoretischen Zusammenhang gebracht.
Author: Geoffrey McLachlan Publisher: John Wiley & Sons ISBN: 047165406X Category : Mathematics Languages : en Pages : 419
Book Description
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: Charles E. McCulloch Publisher: IMS ISBN: 9780940600546 Category : Mathematics Languages : en Pages : 100
Book Description
Wiley Series in Probability and Statistics A modern perspective on mixed models The availability of powerful computing methods in recent decades has thrust linear and nonlinear mixed models into the mainstream of statistical application. This volume offers a modern perspective on generalized, linear, and mixed models, presenting a unified and accessible treatment of the newest statistical methods for analyzing correlated, nonnormally distributed data. As a follow-up to Searle's classic, Linear Models, and Variance Components by Searle, Casella, and McCulloch, this new work progresses from the basic one-way classification to generalized linear mixed models. A variety of statistical methods are explained and illustrated, with an emphasis on maximum likelihood and restricted maximum likelihood. An invaluable resource for applied statisticians and industrial practitioners, as well as students interested in the latest results, Generalized, Linear, and Mixed Models features: * A review of the basics of linear models and linear mixed models * Descriptions of models for nonnormal data, including generalized linear and nonlinear models * Analysis and illustration of techniques for a variety of real data sets * Information on the accommodation of longitudinal data using these models * Coverage of the prediction of realized values of random effects * A discussion of the impact of computing issues on mixed models
Author: Tarek Elguebaly Publisher: ISBN: Category : Languages : en Pages : 0
Book Description
Finite mixture models are among the most useful machine learning techniques and are receiving considerable attention in various applications. The use of finite mixture models in image and signal processing has proved to be of considerable interest in terms of both theoretical development and in their usefulness in several applications. In most of the applications, the Gaussian density is used in the mixture modeling of data. Although a Gaussian mixture may provide a reasonable approximation to many real-world distributions, it is certainly not always the best approximation especially in image and signal processing applications where we often deal with non-Gaussian data. In this thesis, we propose two novel approaches that may be used in modeling non-Gaussian data. These approaches use two highly flexible distributions, the generalized Gaussian distribution (GGD) and the general Beta distribution, in order to model the data. We are motivated by the fact that these distributions are able to fit many distributional shapes and then can be considered as a useful class of flexible models to address several problems and applications involving measurements and features having well-known marked deviation from the Gaussian shape. For the mixture estimation and selection problem, researchers have demonstrated that Bayesian approaches are fully optimal. The Bayesian learning allows the incorporation of prior knowledge in a formal coherent way that avoids overfitting problems. For this reason, we adopt different Bayesian approaches in order to learn our models parameters. First, we present a fully Bayesian approach to analyze finite generalized Gaussian mixture models which incorporate several standard mixtures, such as Laplace and Gaussian. This approach evaluates the posterior distribution and Bayes estimators using a Gibbs sampling algorithm, and selects the number of components in the mixture using the integrated likelihood. We also propose a fully Bayesian approach for finite Beta mixtures learning using a Reversible Jump Markov Chain Monte Carlo (RJMCMC) technique which simultaneously allows cluster assignments, parameters estimation, and the selection of the optimal number of clusters. We then validate the proposed methods by applying them to different image processing applications.
Author: Tatiana V Tatarinova
Author: Tatiana V Tatarinova
Author: Tatiana Tatarinova
Author: Marie Davidian
Author: Marie Davidian
Author: David G. T. Denison
Author: Geoffrey McLachlan
Author: Bareng Aletta Sanny Nonyane
Author: Jeffrey Robert Harring
Author: Charles E. McCulloch
Author: Tarek Elguebaly