Some Distributions on Finite Rooted Binary Trees

2017/08/21 by Sean Cleary, Mareike Fischer, Cleary, Sean +5 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #05C05 #60C05 #Combinatorics (math.CO) #Complex Network Analysis Techniques #Data Management and Algorithms #FOS: Mathematics #Group Theory (math.GR) #Probability (math.PR) #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1708.06130

openalex publication_date 2017/08/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce some natural families of distributions on rooted binary ranked plane trees with a view toward unifying ideas from various fields, including macroevolution, epidemiology, computational group theory, search algorithms and other fields. In the process we introduce the notions of split-exchangeability and plane-invariance of a general Markov splitting model in order to readily obtain probabilities over various equivalence classes of trees that arise in statistics, phylogenetics, epidemiology and group theory.

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