title: Uniformization for sampling realizations of Markov processes: applications to Bayesian implementations of codon substitution models.
abstract: BACKGROUND
  Mapping character state changes over phylogenetic trees is central to the study of evolution. However, current probabilistic methods for generating such mappings are ill-suited to certain types of evolutionary models, in particular, the widely used models of codon substitution.
  
  
  RESULTS
  We describe a general method, based on a uniformization technique, which can be utilized to generate realizations of a Markovian substitution process conditional on an alignment of character states and a given tree topology. The method is applicable under a wide range of evolutionary models, and to illustrate its usefulness in practice, we embed it within a data augmentation-based Markov chain Monte Carlo sampler, for approximating posterior distributions under previously proposed codon substitution models. The sampler is found to be more efficient than the conventional pruning-based sampler with the decorrelation times between draws from the posterior reduced by a factor of 20 or more.
authors.affiliation: Canadian Institute for Advanced Research, Département de Biochimie, Université de Montréal, C.P. 6821, Succ. Centre-ville, Montréal, Québec Canada. nicolas.rodrigue@umontreal.ca
authors.forename: Nicolas
authors.initials: N
authors.lastname: Rodrigue
authors.forename: Hervé
authors.initials: H
authors.lastname: Philippe
authors.forename: Nicolas
authors.initials: N
authors.lastname: Lartillot
mesh_terms: D000465:Algorithms; D001499:Bayes Theorem; D002874:Chromosome Mapping / Q000379:methods*; D003062:Codon / Q000235:genetics*; D003198:Computer Simulation; D019143:Evolution, Molecular; D008390:Markov Chains; D008957:Models, Genetic; D015233:Models, Statistical; D010363:Pattern Recognition, Automated / Q000379:methods; D010802:Phylogeny; D018401:Sample Size; D016415:Sequence Alignment / Q000379:methods*; D017422:Sequence Analysis, DNA / Q000379:methods*
chemical_list: D003062:Codon