JSM 2011 Online Program

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Abstract Details

Activity Number: 170
Type: Contributed
Date/Time: Monday, August 1, 2011 : 10:30 AM to 12:20 PM
Sponsor: Biometrics Section
Abstract - #303185
Title: Mixing Times for a Class of Markov Chains on Phylogenetic Tree Spaces
Author(s): David Allen Spade*+ and Radu Herbei and Laura Kubatko
Companies: The Ohio State University and The Ohio State University and The Ohio State University
Address: Department of Statistics, Columbus, OH, 43210,
Keywords: Markov Chains ; Phylogenetic trees ; Mixing Times
Abstract:

In the past decade, there has been a considerable amount of work done in studying the mixing time for Markov chains on phylogenetic trees. In the current work we extend existing results to Markov chains that are commonly used in algorithms for phylogenetic inference. Specifically, we study NNI, SPR and TBR moves on rooted and unrooted trees with n taxa. For such trees we estimate the total variation distance between the law of the current state and the stationary law in some simple cases and provide upper and lower bounds for this distance in the general case. We will also perform some simulations to investigate how well the bounds behave.


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