Subtree prune and regraft: A reversible real tree-valued Markov process

Evans, Steven N.; Winter, Anita

Ann. Probab., Tome 34 (2006) no. 1, p. 918-961 / Harvested from Project Euclid

Résumé

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.

Publié le : 2006-05-14
Classification: Dirichlet form, continuum random tree, Brownian excursion, phylogenetic tree, Markov chain Monte Carlo, simulated annealing, path decomposition, excursion theory, Gromov–Hausdorff metric, Prohorov metric, 60J25, 60J75, 92B10

@article{1151418488,
     author = {Evans, Steven N. and Winter, Anita},
     title = {Subtree prune and regraft: A reversible real tree-valued Markov process},
     journal = {Ann. Probab.},
     volume = {34},
     number = {1},
     year = {2006},
     pages = { 918-961},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1151418488}
}

Evans, Steven N.; Winter, Anita. Subtree prune and regraft: A reversible real tree-valued Markov process. Ann. Probab., Tome 34 (2006) no. 1, pp.  918-961. http://gdmltest.u-ga.fr/item/1151418488/