A Multivariate Volume Depth for Image Data Analysis

• Activity Number: 674
• Type: Topic Contributed
• Date/Time: Thursday, August 13, 2015 : 10:30 AM to 12:20 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Sara Lopez-Pintado*
• Companies: Columbia University
• Keywords: Depth ; image data ; nonparametric statistics ; robust ; multivariate functional data ; rank test

Abstract

Biomedical diagnosis is increasingly reliant on more complex data. In some applications the data consists of several correlated functions for each sample subject. For example, multiple leads recordings from an electrocardiogram or multiple brain images for each subject, such as functional magnetic resonance imaging (fMRI) recordings of different neurophysiological states for each subject. Developing new statistical tools to analyze these rich data sets has become a limiting factor for the advancement of many disciplines. In the applications mentioned above the basic unit of observation can be considered as a general function which is defined in a subset of either the real line or a higher dimensional space and takes values in a multivariate space. In this project we propose a general definition of depth for arbitrary general functions called multivariate modified volume depth. The theoretical properties of this depth will be established and it will be used as a building block for developing robust statistical methods for images. We propose two depth-based nonparametric tests for comparing brain images from healthy individuals and patients with major depressive disorders.