2005/05/31 by Elchanan Mossel, Eric Vigoda · 1 citation
Biochemistry, Genetics and Molecular Biology · Computer Science · Earth and Planetary Sciences · #Bayesian Methods and Mixture Models #Evolution and Paleontology Studies #Genomics and Phylogenetic Studies #msc:60J10 #msc:92D15 #q-bio.GN #q-bio.PE
paper · pdf · doi:10.1214/105051600000000538
published as Annals of Applied Probability 2006, Vol. 16, No. 4, 2215-2234 · Published at http://dx.doi.org/10.1214/105051600000000538 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)
openalex publication_date 2006/11/01 · arxiv created 2007/02/14 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.