test Browse by Author Names Browse by Titles of Works Browse by Subjects of Works Browse by Issue Dates of Works
       

Advanced Search
Home   
 
Browse   
Communities
& Collections
  
Issue Date   
Author   
Title   
Subject   
 
Sign on to:   
Receive email
updates
  
My Account
authorized users
  
Edit Profile   
 
Help   
About T-Space   

T-Space at The University of Toronto Libraries >
School of Graduate Studies - Theses >
Doctoral >

Please use this identifier to cite or link to this item: http://hdl.handle.net/1807/24831

Title: Bayesian Methods in Gaussian Graphical Models
Authors: Mitsakakis, Nikolaos
Advisor: Escobar, Michael
Massam, Helene
Department: Dalla Lana School of Public Health
Keywords: Gaussian Graphical Models
DY-conjugate prior
Markov Chain Monte Carlo
Model Selection
Normalizing constant
Metropolis Hastings
Bayes Factors
Deviance Information Criterion
Issue Date: 31-Aug-2010
Abstract: This thesis contributes to the field of Gaussian Graphical Models by exploring either numerically or theoretically various topics of Bayesian Methods in Gaussian Graphical Models and by providing a number of interesting results, the further exploration of which would be promising, pointing to numerous future research directions. Gaussian Graphical Models are statistical methods for the investigation and representation of interdependencies between components of continuous random vectors. This thesis aims to investigate some issues related to the application of Bayesian methods for Gaussian Graphical Models. We adopt the popular $G$-Wishart conjugate prior $W_G(\delta,D)$ for the precision matrix. We propose an efficient sampling method for the $G$-Wishart distribution based on the Metropolis Hastings algorithm and show its validity through a number of numerical experiments. We show that this method can be easily used to estimate the Deviance Information Criterion, providing a computationally inexpensive approach for model selection. In addition, we look at the marginal likelihood of a graphical model given a set of data. This is proportional to the ratio of the posterior over the prior normalizing constant. We explore methods for the estimation of this ratio, focusing primarily on applying the Monte Carlo simulation method of path sampling. We also explore numerically the effect of the completion of the incomplete matrix $D^{\mathcal{V}}$, hyperparameter of the $G$-Wishart distribution, for the estimation of the normalizing constant. We also derive a series of exact and approximate expressions for the Bayes Factor between two graphs that differ by one edge. A new theoretical result regarding the limit of the normalizing constant multiplied by the hyperparameter $\delta$ is given and its implications to the validity of an improper prior and of the subsequent Bayes Factor are discussed.
URI: http://hdl.handle.net/1807/24831
Appears in Collections:Doctoral
Dalla Lana School of Public Health - Doctoral theses

Files in This Item:

File Description SizeFormat
Mitsakakis_Nikolaos_201006_PhD_Thesis.pdf1.16 MBAdobe PDF
View/Open

Items in T-Space are protected by copyright, with all rights reserved, unless otherwise indicated.

uoft