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Limitations of Markov chain Monte Carlo algorithms for Bayesian inference of phylogeny. (English) Zbl 1121.60078
Summary: Markov chain Monte Carlo algorithms play a key role in the Bayesian approach to phylogenetic inference. 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.
Reviewer: Reviewer (Berlin)

MSC:
60J10 Markov chains (discrete-time Markov processes on discrete state spaces)
92D15 Problems related to evolution
Software:
MrBayes
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