2019/02/08 by Ben Hollering, Hollering, Ben, Seth Sullivant +1
Computer Science · Mathematics · #05C05 (Primary) #60C05 (Secondary) #92B10 (Secondary) #Bayesian Methods and Mixture Models #Bayesian Modeling and Causal Inference #Combinatorics (math.CO) #FOS: Biological sciences #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Populations and Evolution (q-bio.PE) #Probability (math.PR)
paper · pdf · doi:10.48550/arxiv.1902.03321
openalex publication_date 2019/02/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce a notion of finite sampling consistency for phylogenetic trees and show that the set of finitely sampling consistent and exchangeable distributions on n leaf phylogenetic trees is a polytope. We use this polytope to show that the set of all exchangeable and infinite sampling consistent distributions on 4 leaf phylogenetic trees is exactly Aldous' beta-splitting model and give a description of some of the vertices for the polytope of distributions on 5 leaves. We also introduce a new semialgebraic set of exchangeable and sampling consistent models we call the multinomial model and use it to characterize the set of exchangeable and sampling consistent distributions.