Detecting Jumps on a Tree: a Hierarchical Normalized Stable Process Model for Evolution of Discrete Distributions

Abstract

This work focuses on clustering populations whose hierarchical dependency structure can be described by a tree. A particular example that is the focus of this work is a phylogenetic tree, whose nodes represent different biological species. In this problem, clustering the populations at the leaves of the tree is equivalent to identifying branches in the tree where the populations at the parent and child node have significantly different distributions. We construct a nonparametric Bayesian model based on the hierarchical normalized stable process and the Poisson process to exploit this hierarchical structure, with a key contribution being the ability to share statistical information between subpopulations. We develop an efficient particle MCMC algorithm to address computational challenges involved with posterior inference. We illustrate the efficacy of our proposed approach on both synthetic and real-world problems.

28 pages, 15 figures