Open Access
May 2006 Subtree prune and regraft: A reversible real tree-valued Markov process
Steven N. Evans, Anita Winter
Ann. Probab. 34(3): 918-961 (May 2006). DOI: 10.1214/009117906000000034


We use Dirichlet form methods to construct and analyze a reversible Markov process, the stationary distribution of which is the Brownian continuum random tree. This process is inspired by the subtree prune and regraft (SPR) Markov chains that appear in phylogenetic analysis.

A key technical ingredient in this work is the use of a novel Gromov–Hausdorff type distance to metrize the space whose elements are compact real trees equipped with a probability measure. Also, the investigation of the Dirichlet form hinges on a new path decomposition of the Brownian excursion.


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Steven N. Evans. Anita Winter. "Subtree prune and regraft: A reversible real tree-valued Markov process." Ann. Probab. 34 (3) 918 - 961, May 2006.


Published: May 2006
First available in Project Euclid: 27 June 2006

zbMATH: 1101.60054
MathSciNet: MR2243874
Digital Object Identifier: 10.1214/009117906000000034

Primary: 60J25 , 60J75
Secondary: 92B10

Keywords: Brownian excursion , Continuum random tree , Dirichlet form , Excursion theory , Gromov–Hausdorff metric , Markov chain Monte Carlo , Path decomposition , phylogenetic tree , Prohorov metric , simulated annealing

Rights: Copyright © 2006 Institute of Mathematical Statistics

Vol.34 • No. 3 • May 2006
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