Biostatistics Seminar Series - Julia Palacios, PhD

Title:Distance-based summaries and modeling of ranked tree shapes and ranked hierarchical clustering trees Abstract: Rooted and ranked binary trees are mathematical objects of great importance used to model hierarchical data and evolutionary processes with applications ranging across many fields including evolutionary biology and infectious disease transmission. While Bayesian methods allow exploration of the posterior distribution of trees, assessing uncertainty and summarizing tree distributions remains challenging for these types of structures. Similarly, in many instances, one seeks to summarize samples of trees obtained with different methods, or from different samples and environments, and wishes to assess stability and generalizability of these summaries. In this talk I will present new metrics on the space of ranked tree shapes and ranked genealogies and provide an efficient combinatorial optimization algorithm for estimating Fréchet means and variances. I will show the applicability of our summary statistics for studying popular tree distributions and for studying the evolution of SARS-CoV-2.