17. Hidden Markov Random Field Models for Network-Based Analysis of Genomic Data

Graphs and networks are common ways of depicting biological information. In biology, many different biological processes are represented by graphs, such as regulatory networks, metabolic pathways and protein-protein interaction networks. This kind of a priori use of graphs is a useful supplement to the standard numerical data such as microarray gene expression data and single nucleotide polymorphisms (SNPs) data. How to incorporate such a prior network information into analysis of numerical data raises interesting statistical problems. Representing the genetic networks as undirected graphs, we have developed several approaches for identifying differentially expressed genes and genes or SNPs associated with diseases in a unified framework of hidden Markov random field (HMRF) models. Different from the traditional empirical Bayes approaches for analysis of gene expression data, the HMRF-based models account for the prior dependency among the genes on the network and therefore effectively utilize the prior network information in identifying the subnetworks of genes that are perturbed by experimental conditions. In this paper, we briefly review the basic setup of the HMRF models and the emission probability functions for some problems often encountered in analysis of microarray gene expression and SNPs data. We also present some interesting areas that require further research.