Some Distributions on Finite Rooted Binary Trees

TL;DR

This paper introduces new distributions on finite rooted binary trees, unifying concepts across multiple fields by defining split-exchangeability and plane-invariance in Markov models to compute probabilities efficiently.

Contribution

It presents a unified framework for distributions on rooted binary trees using Markov models with novel invariance properties, applicable across diverse scientific disciplines.

Findings

Defined split-exchangeability and plane-invariance for Markov models

Developed methods to compute probabilities over tree equivalence classes

Unified approaches across phylogenetics, epidemiology, and group theory

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.