Bayesian Gaussian Graphical models using sparse selection priors and their mixtures
Bayesian Gaussian Graphical Models Using Sparse Selection Priors and Their Mixtures. (August 2011) Rajesh Talluri, B.Tech. Indian Institute of Technology, Guwahati Co Chairs of Advisory Committee: Dr. Bani K. Mallick Dr. Veerabhadran Baladandayuthapani We propose Bayesian methods for estimating the precision matrix in Gaussian graphical models. The methods lead to sparse and adaptively shrunk estimators of the precision matrix, and thus conduct model selection and estimation simultaneously. Our methods are based on selection and shrinkage priors leading to parsimonious parameterization of the precision (inverse covariance) matrix, which is essential in several applications in learning relationships among the variables. In Chapter I, we employ the Laplace prior on the off diagonal element of the precision matrix, which is similar to the lasso model in a regression context. This type of prior encourages sparsity while providing shrinkage estimates. Secondly we introduce a novel type of selection prior that develops a sparse structure of the precision matrix by making most of the elements exactly zero, ensuring positive definiteness. In Chapter II we extend the above methods to perform classification. Reversephase protein array (RPPA) analysis is a powerful, relatively new platform that allows for high throughput, quantitative analysis of protein networks. One of the challenges that currently limits the potential of this technology is the lack of methods that allows for accurate data modeling and identification of related networks and samples. Such models may improve the accuracy of biological sample classification based on patterns of protein network activation, and provide insight into the distinct biological relationships underlying different cancers. We propose a Bayesian sparse graphical modeling