GENERALIZED MARKOV BRANCHING TREES

被引：2

作者：

Crane, Harry ^{[1
]}

机构：

[1] Rutgers State Univ, Dept Stat & Biostat, 110 Frelinghuysen Rd, Piscataway, NJ 08854 USA

来源：

ADVANCES IN APPLIED PROBABILITY | 2017年 / 49卷 / 01期

关键词：

Markov branching tree; exchangeable random partition; exchangeable fragmentation; beta-splitting model; coalescent process; hidden Markov model; GALTON-WATSON; RANDOM PARTITIONS; RECOMBINATION; DISTRIBUTIONS; CHAINS; MODELS;

D O I：

10.1017/apr.2016.81

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

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.

引用

页码：108 / 133

页数：26

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