Detecting Jumps on a Tree: a Hierarchical Pitman-Yor Model for Evolution of Phenotypic Distributions

Abstract: This work focuses on clustering populations with a hierarchical dependency structure that can be described by a tree. A particular example that is the focus of our work is the phylogenetic tree, with nodes often representing biological species. Clustering of the populations in this problem is equivalent to identify 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 hierarchical Pitman-Yor and Poisson processes 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.