- Salón K201 en CIMAT, Guanajuato.
13:00-14:00 horas. Tropical Statistics for Phylogenetic Trees
Anthea Monod (Columbia University)
Resumen: Phylogenetic trees are the fundamental mathematical representation of evolutionary processes in biology. As data objects, they are characterized by the challenges associated with "big data," as well as the complication that their discrete geometric structure results in a non-Euclidean phylogenetic tree space, which poses computational and statistical limitations. We propose a novel framework constructed from tropical geometry for the statistical analysis of evolutionary biological processes represented by sets of phylogenetic trees. Our structure allows for the definition of probability measures, expectations, variances, and other fundamental statistical quantities. In addition, our setting exhibits analytic, geometric, and topological properties that are desirable for rigorous theoretical treatment in probability and statistics, as well as increased computational efficiency over the current state-of-the-art. We demonstrate our approach and compare against the current standard on seasonal influenza data. This is joint work with Bo Lin (Georgia Tech), Qiwen Kang (University of Kentucky), and Ruriko Yoshida (Naval Postgraduate School).