Multi-Resolution Two-Sample Comparison Through the Divide-Merge Markov Tree

• Activity Number: 20
• Type: Topic Contributed
• Date/Time: Sunday, August 3, 2014 : 2:00 PM to 3:50 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Li Ma*+ and Jacopo Soriano
• Companies: Duke University and Duke University
• Keywords: Bayesian inference ; two-sample comparison ; nonparametrics ; multi-resolution inference ; recursive partition ; flow cytometry

Abstract

We introduce a probabilistic framework for two-sample comparison based on a nonparametric process taking the form of a Markov model that transitions between a "divide" and a "merge" state on a multi-resolution partition tree of the sample space. Multi-scale two-sample comparison is achieved through inferring the state of the process along the partition tree. The Markov design allows the process to incorporate spatial clustering of differential structures, which is commonly observed but ignored by existing methods. Further, a random partition mechanism is incorporated to allow the partition tree to be data-adaptive. Inference is carried out under the Bayesian paradigm through recursive propagation algorithms. We demonstrate our method through numerical examples, showing that it substantially outperforms other state-of-the-art two-sample tests in several settings. We establish the asymptotic consistency for our method, and propose an approach to visualizing the scale and location of the identified differences. We apply our method to a 7-d flow cytometry data set, and successfully identify a scientifically validated local differential hotspot involving less than 1% of the data points.