ISBN: STANFORD:rg499mj4337

Category: Unavailable

Page count: 117

Testing and characterizing the difference between two data samples is of fundamental interest in statistics. Existing methods such as Kolmogorov-Smirnov and Cramer- von-Mises tests do not scale well as the dimensionality increases and provide no easy way to characterize the difference should it exist. In this work, we propose a theoretical framework for inference that addresses these challenges in the form of a prior for Bayesian nonparametric analysis. The new prior is constructed based on a random-partition-and-assignment procedure similar to the one that defines the standard optional P´olya tree distribution, but has the ability to generate multiple random distributions jointly. These random probability distributions are allowed to "couple", that is to have the same conditional distribution, on subsets of the sample space. We show that this "coupling optional P´olya tree" prior provides a convenient and effective way for both the testing of two sample difference and the learning of the underlying structure of the difference. We provide both simulated and real data examples to illustrate the work of this method and compare its performance to several existing methods, both frequentist and Bayesian. We demonstrate through an analysis of the Wellcome Trust Case-control Consortium data how the method can be applied to conduct multiple marker association tests. We also discuss some practical issues in the computational implementation of this prior and explore techniques that can be utilized to improve the computational efficiency in the appendices.