Testing for or Against a Union-of-Cones Hypothesis with Applications to Genomic Data Analysis

• Activity Number: 325
• Type: Invited
• Date/Time: Tuesday, August 2, 2011 : 10:30 AM to 12:20 PM
• Sponsor: Council of Chapters
• Author(s): Dan Nettleton*+
• Companies: Iowa State University
• Keywords: order restricted inference ; multiple testing ; microarray ; gene expression

Abstract

In some genomics applications, it is natural for either a null hypothesis or an alternative hypothesis to constrain a parameter vector to a union of cones. Although there is a long history of results from order restricted inference that apply when a parameter vector is constrained to a cone, relatively little work has been done for the union-of-cones case. We will discuss unique features of estimation and hypothesis testing when either the null hypothesis or the alternative hypothesis constrains a parameter vector to a union of cones. Two example applications from genomics will be presented. The first application involves identifying differentially expressed gene sets by searching for monotonic changes in multivariate gene expression distributions. This is relevant for experiments were the multivariate expression distribution of the set of genes is measured for each level of a naturally ordered covariate like time or dose of a drug. A second application involves identifying genes that show evidence of heterosis (hybrid vigor) for gene expression traits when analyzing data from parental inbred lines and their hybrid offspring.