Identifying differentially expressed genes using the Polya urn scheme

Abstract

A common interest in gene expression data analysis is to identify genes that present significant changes in expression levels among biological experimental conditions. In this paper, we develop a Bayesian approach to make a gene-by-gene comparison in the case with a control and more than one treatment experimental condition. The proposed approach is within a Bayesian framework with a Dirichlet process prior. The comparison procedure is based on a model selection procedure developed using the discreteness of the Dirichlet process and its representation via Polya urn scheme. The posterior probabilities for models considered are calculated using a Gibbs sampling algorithm. A numerical simulation study is conducted to understand and compare the performance of the proposed method in relation to usual methods based on analysis of variance (ANOVA) followed by a Tukey test. The comparison among methods is made in terms of a true positive rate and false discovery rate. We find that proposed method outperforms the other methods based on ANOVA followed by a Tukey test. We also apply the methodologies to a publicly available data set on Plasmodium falciparum protein.

Comparative Analysis of Improved Dirichlet Process Mixture Model

“…The Dirichlet process, as a random process, is used as the prior distribution for Bayesian nonparametric statistics. In order to sample from the Dirichlet process, three different constructions have been proposed: the Polya urn scheme [7], the Chinese restaurant process (CRP) [8], and stick-breaking [9], making it possible to apply this process in various applications. Models based on the Dirichlet process can adaptively determine the number of clusters based on the data, thereby solving the problem of determining the number of clusters.…”