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Subtree prune and re-graft: a reversible real tree valued Markov process | | Steven N. Evans
; Anita Winter
; | | Date: |
11 Feb 2005 | | Subject: | Probability; Metric Geometry; Populations and Evolution; Quantitative Methods MSC-class: 60J25; 60J75; 92B10 | math.PR math.MG q-bio.PE q-bio.QM | | Abstract: | 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 re-graft (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. | | Source: | arXiv, math.PR/0502226 | | Services: | Forum | Review | PDF | Favorites | |
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