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Probabilistic Graphical Models for Genetics, Genomics, and Postgenomics$
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Christine Sinoquet and Raphaël Mourad

Print publication date: 2014

Print ISBN-13: 9780198709022

Published to Oxford Scholarship Online: December 2014

DOI: 10.1093/acprof:oso/9780198709022.001.0001

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Graphical Models and Multivariate Analysis of Microarray Data

Graphical Models and Multivariate Analysis of Microarray Data

Chapter:
(p.85) Chapter 3 Graphical Models and Multivariate Analysis of Microarray Data
Source:
Probabilistic Graphical Models for Genetics, Genomics, and Postgenomics
Author(s):

Harri Kiiveri

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198709022.003.0003

The usual analysis of gene expression data ignores the correlation between gene expression values. Biologically, this assumption is unreasonable. The approach presented in this chapter allows for correlation between genes through a sparse Gaussian graphical model: sparse inverse covariance matrices and their associated graphical representations are used to capture the notion of gene networks. Existing methods find their limitations in the issue posed by the identification of the pattern of zeroes in such inverse covariance matrices. A workable solution for determining the zero pattern is provided in this chapter. Two other important contributions of this chapter are a method for very high-dimensional model fitting and a distribution-free approach to hypothesis testing. Such tests address assessment of differential expression and of differential connection, a novel notion introduced in this chapter. An example dealing with real data is presented.

Keywords:   gene network, microarray, Gaussian graphical models, inverse covariance matrix, sparse matrix

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