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## Details

Genre/Form: | Electronic books |
---|---|

Additional Physical Format: | Print version: Tatarinova, Tatiana V. Nonlinear mixture models. London : Imperial College Press, [2015] (DLC) 2014038898 (OCoLC)701806866 |

Material Type: | Document, Internet resource |

Document Type: | Internet Resource, Computer File |

All Authors / Contributors: |
Tatiana V Tatarinova; Alan Schumitzky |

ISBN: | 9781848167575 1848167571 |

OCLC Number: | 900633207 |

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. |

Responsibility: | Tatiana Tatarinova, University of Glamorgan, UK, Alan Schumitzky, University of Southern California, USA. |

### Abstract:

Provides an introduction to the important subject of nonlinear mixture models from a Bayesian perspective. This title contains background material, a brief description of Markov chain theory, as well as novel algorithms and their applications.
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