Limitations of Markov chain Monte Carlo algorithms for Bayesian Inference of phylogeny

Details Limitations of Markov chain Monte Carlo algorithms for Bayesian Inference of phylogeny Limitations of Markov chain Monte Carlo algorithms for Bayesian Inference of phylogeny

2005-05-02

arxiv.org/abs/q-bio/0505002v5

Annals of Applied Probability 2006, Vol. 16, No. 4, 2215-2234

Biology

Quantitative Biology

Populations and Evolution

Published at http://dx.doi.org/10.1214/105051600000000538 in the Annals of Applied Probability (http://www.imstat.org/aap/) by

Scientific paper

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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