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Generalized Markov branching trees

Part of: Stochastic processes

Published online by Cambridge University Press:  17 March 2017

Harry Crane
Harry Crane*
Affiliation:
Rutgers University
*
* Postal address: Department of Statistics and Biostatistics, Rutgers University, 110 Frelinghuysen Road, Piscataway, NJ 08854, USA. Email address: hcrane@stat.rutgers.edu
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Abstract

Motivated by the gene tree/species tree problem from statistical phylogenetics, we extend the class of Markov branching trees to a parametric family of distributions on fragmentation trees that satisfies a generalized Markov branching property. The main theorems establish important statistical properties of this model, specifically necessary and sufficient conditions under which a family of trees can be constructed consistently as sample size grows. We also consider the question of attaching random edge lengths to these trees.

Keywords

Markov branching treeexchangeable random partitionexchangeable fragmentationbeta-splitting modelcoalescent processhidden Markov model

MSC classification

Primary: 60G09: Exchangeability 60G05: Foundations of stochastic processes
Secondary: 92D10: Genetics
Type
Research Article
Information
Advances in Applied Probability , Volume 49 , Issue 1 , March 2017 , pp. 108 - 133
Copyright
Copyright © Applied Probability Trust 2017 

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