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November 2006 Limitations of Markov chain Monte Carlo algorithms for Bayesian inference of phylogeny
Elchanan Mossel, Eric Vigoda
Ann. Appl. Probab. 16(4): 2215-2234 (November 2006). DOI: 10.1214/105051600000000538


Markov chain Monte Carlo algorithms play a key role in the Bayesian approach to phylogenetic inference. In this paper, we present the first theoretical work analyzing the rate of convergence of several Markov chains widely used in phylogenetic inference. We analyze simple, realistic examples where these Markov chains fail to converge quickly. In particular, the data studied are generated from a pair of trees, under a standard evolutionary model. We prove that many of the popular Markov chains take exponentially long to reach their stationary distribution. Our construction is pertinent since it is well known that phylogenetic trees for genes may differ within a single organism. Our results shed a cautionary light on phylogenetic analysis using Bayesian inference and highlight future directions for potential theoretical work.


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Elchanan Mossel. Eric Vigoda. "Limitations of Markov chain Monte Carlo algorithms for Bayesian inference of phylogeny." Ann. Appl. Probab. 16 (4) 2215 - 2234, November 2006.


Published: November 2006
First available in Project Euclid: 17 January 2007

zbMATH: 1121.60078
MathSciNet: MR2288719
Digital Object Identifier: 10.1214/105051600000000538

Primary: 60J10, 92D15

Rights: Copyright © 2006 Institute of Mathematical Statistics


Vol.16 • No. 4 • November 2006
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