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Bayesian analysis of linear and nonl...

Tatarinova, Tatiana.

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Bayesian analysis of linear and nonlinear mixture models.

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Bayesian analysis of linear and nonlinear mixture models./
Author:	Tatarinova, Tatiana.
Description:	301 p.
Notes:	Adviser: Alan Schumitzky.
Contained By:	Dissertation Abstracts International67-10B.
Subject:	Mathematics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3237171
ISBN:	9780542912771

Bayesian analysis of linear and nonlinear mixture models.
Tatarinova, Tatiana.

Bayesian analysis of linear and nonlinear mixture models. - 301 p.

Adviser: Alan Schumitzky.

Thesis (Ph.D.)--University of Southern California, 2006.

In this thesis we study Bayesian analysis of nonlinear hierarchical mixture models with a finite but possibly unknown number of components. Our approach will be based on Monte Carlo Markov Chain (MCMC) methods. Application of our methods will be directed to problems in gene expression analysis and population pharmacokinetics in which these nonlinear mixture models arise very naturally. For gene expression data, one application will be to determine which genes should be associated with the same component of the mixture (clustering problem). For population pharmacokinetics, the nonlinear mixture model, based on previous clinical data, becomes the prior distribution for individual therapy. Then Bayesian analysis of prediction and control can be performed. From a mathematical and statistical point of view, these are the problems analyzed in this thesis: (1) Theoretical and practical convergence problems of the MCMC method; (2) Clustering problems; (3) Determination of the number of components in the mixture (4) Computational problems associated with likelihood calculations.

ISBN: 9780542912771Subjects--Topical Terms:

515831
Mathematics.

Bayesian analysis of linear and nonlinear mixture models.
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020 $a 9780542912771
035 $a (UnM)AAI3237171
035 $a AAI3237171
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100 1 $a Tatarinova, Tatiana. $3 1292942
245 1 0 $a Bayesian analysis of linear and nonlinear mixture models.
300 $a 301 p.
500 $a Adviser: Alan Schumitzky.
500 $a Source: Dissertation Abstracts International, Volume: 67-10, Section: B, page: 5796.
502 $a Thesis (Ph.D.)--University of Southern California, 2006.
520 $a In this thesis we study Bayesian analysis of nonlinear hierarchical mixture models with a finite but possibly unknown number of components. Our approach will be based on Monte Carlo Markov Chain (MCMC) methods. Application of our methods will be directed to problems in gene expression analysis and population pharmacokinetics in which these nonlinear mixture models arise very naturally. For gene expression data, one application will be to determine which genes should be associated with the same component of the mixture (clustering problem). For population pharmacokinetics, the nonlinear mixture model, based on previous clinical data, becomes the prior distribution for individual therapy. Then Bayesian analysis of prediction and control can be performed. From a mathematical and statistical point of view, these are the problems analyzed in this thesis: (1) Theoretical and practical convergence problems of the MCMC method; (2) Clustering problems; (3) Determination of the number of components in the mixture (4) Computational problems associated with likelihood calculations.
520 $a In the statistical literature, these problems have mainly been addressed in the linear case. Developing methods for the nonlinear case is one of the main contributions of this thesis. The problem of determining which mixture component an observation is most likely to come from (clustering problem) is very important in analyzing gene expression data and it will be studied in this thesis. We have studied convergence of the resulting Markov chain. In particular, we proved that this method generates an irreducible Markov chain. This theoretically implies that the chain visits all parts of the posterior distribution surface. Practically, the resulting Markov chain can get computationally trapped in a local region of the posterior surface and cannot escape. Developing methods to avoid this problem are proposed.
520 $a It will be shown that in order to fix the problem of "trapping", the computed posterior distribution will be forced to be symmetric relative to all components of the mixture. Consequently an observation will equally be likely to come from any component. Clustering must then be done outside of the MCMC method. In this thesis we proposed two novel trans-dimensional methods: Kullback-Leibler MCMC and Multiple Collapse Clustering.
590 $a School code: 0208.
650 4 $a Mathematics. $3 515831
690 $a 0405
710 2 0 $a University of Southern California. $3 700129
773 0 $t Dissertation Abstracts International $g 67-10B.
790 $a 0208
790 1 0 $a Schumitzky, Alan, $e advisor
791 $a Ph.D.
792 $a 2006
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3237171