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2013 Central limit theorems for Fréchet means in the space of phylogenetic trees
Dennis Barden, Huiling Le, Megan Owen
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Electron. J. Probab. 18: 1-25 (2013). DOI: 10.1214/EJP.v18-2201


This paper studies the characterisation, and the limiting distributions, of Fréchet means in the space of phylogenetic trees. This space is topologically stratified, as well as being a CAT(0) space. We use a generalised version of the Delta method to demonstrate non-classical behaviour arising from the global topological structure of the space. In particular, we show that, for the space of trees with four leaves, although they are related to the Gaussian distribution, the forms taken by the limiting distributions depend on the co-dimensions of the strata in which the Fréchet means lie.


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Dennis Barden. Huiling Le. Megan Owen. "Central limit theorems for Fréchet means in the space of phylogenetic trees." Electron. J. Probab. 18 1 - 25, 2013.


Accepted: 16 February 2013; Published: 2013
First available in Project Euclid: 4 June 2016

zbMATH: 1284.60023
MathSciNet: MR3035753
Digital Object Identifier: 10.1214/EJP.v18-2201

Primary: 60D05
Secondary: 60F05

Keywords: central limit theorem , Frechet mean , phylogenetic trees , stratified manifold

Vol.18 • 2013
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