Phylogenetic MCMC algorithms are misleading on mixtures of trees.

@article{Mossel2005PhylogeneticMA,
  title={Phylogenetic MCMC algorithms are misleading on mixtures of trees.},
  author={Elchanan Mossel and Eric Vigoda},
  journal={Science},
  year={2005},
  volume={309 5744},
  pages={2207-9}
}
Markov chain Monte Carlo (MCMC) algorithms play a critical role in the Bayesian approach to phylogenetic inference. We present a theoretical analysis of the rate of convergence of many of the widely used Markov chains. For N characters generated from a uniform mixture of two trees, we prove that the Markov chains take an exponentially long (in N) number of iterations to converge to the posterior distribution. Nevertheless, the likelihood plots for sample runs of the Markov chains deceivingly… CONTINUE READING

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