Title Nonlinear mixture models : a bayesian approach / Tatiana Tatarinova, University of Glamorgan, UK, Alan Schumitzky, University of Southern California, USA

Published Hackensack, NJ : Imperial College Press, [2015] ©2015

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Description 1 online resource (xxiv, 269 pages) : illustrations Contents 1. Introduction. 1.1. Bayesian approach. 1.2. Review of applications of mixture models in population pharmacokinetics. 1.3. Review of applications of mixture models to problems in computational biology. 1.4. Outline of the book -- 2. Mathematical description of nonlinear mixture models. 2.1. Fundamental notions of Markov chain Monte Carlo. 2.2. Nonlinear hierarchical models. 2.3. Gibbs sampling. 2.4. Prior distributions: Linear and nonlinear cases -- 3. Label switching and trapping. 3.1. Label switching and permutation invariance. 3.2. Markov chain convergence. 3.3. Random permutation sampler. 3.4. Re-parametrization. 3.5. Stephens' approach: Relabeling strategies 4. Treatment of mixture models with an unknown number of components. 4.1. Introduction. 4.2. Finding the optimal number of components using weighted Kullback-Leibler distance. 4.3. Stephens' approach: Birth-death Markov chain Monte Carlo. 4.4. Kullback-Leibler Markov chain Monte Carlo -- A new algorithmfor finite mixture analysis -- 5. Applications of BDMCMC, KLMCMC, and RPS. 5.1. Galaxy data. 5.2. Simulated nonlinear normal mixture model. 5.3. Linear normal mixture model: Boys and girls. 5.4. Nonlinear pharmacokinetics model and selection of prior distributions. 5.5. Nonlinear mixture models in gene expression studies 6. Nonparametric methods. 6.1. Definition of the basic model. 6.2. Nonparametric maximum likelihood. 6.3. Nonparametric Bayesian approach. 6.4. Gibbs sampler for the Dirichlet process. 6.5. Nonparametric Bayesian examples. 6.6. Technical notes. 6.7. Stick-breaking priors. 6.8. Examples of stick-breaking. 6.9. Maximum likelihood and stick-breaking (A connection between NPML and NPB approaches) -- 7. Bayesian clustering methods. 7.1. Brief review of clustering methods in microarray analysis. 7.2. Application of KLMCMC to gene expression time-series analysis. 7.3. Kullback-Leibler clustering. 7.4. Simulated time-series data with an unknown number of components (Zhou model). 7.5. Transcription start sites prediction. 7.6. Conclusions Summary 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 Bibliography Includes bibliographical references (pages 255-266) and index Notes Print version record Subject Markov processes. Bayesian statistical decision theory. Nonparametric statistics. Multivariate analysis. Markov Chains Statistics, Nonparametric Multivariate Analysis MATHEMATICS -- Applied. MATHEMATICS -- Probability & Statistics -- General. Bayesian statistical decision theory Markov processes Multivariate analysis Nonparametric statistics Form Electronic book Author Schumitzky, Alan, author. ISBN 9781848167575 1848167571

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