Modelos grafos para expressão gênica

Abstract

The purpose of this work is to examine statistical methodologies that can be applied to problems that involve a large number of variables using as a tool graphical models that assist on the visualization of the conditional independency and dependency structure, thus a graphical model represents the relationship between random variables (dependence, independence and conditional independence), each node is a random variable and the edges between the nodes are different ways they relate to each other. This dissertation studies Gaussian graphical models. We use methodologies for large scale models (\large p and small n") used on the analysis of gene association from gene expression data. We describe the sparse graphical models and we implement a computational algorithm. We veriffed a Bayesian approach using the Reversible Jump MCMC. We also introduce decomposable graphical models in relation to the computational effciency attained by the decomposition of the sample space, and we found the best decomposable graph based on the Metropolis-Hastings algorithm for a real data set.