Bayesian Phylogenetic Inference via Markov Chain Monte Carlo Methods

@article{Mau1999BayesianPI,
  title={Bayesian Phylogenetic Inference via Markov Chain Monte Carlo Methods},
  author={Bob Mau and Michael A. Newton and Bret R. Larget},
  journal={Biometrics},
  year={1999},
  volume={55}
}
Summary. We derive a Markov chain to sample from the posterior distribution for a phylogenetic tree given sequence information from the corresponding set of organisms, a stochastic model for these data, and a prior distribution on the space of trees. A transformation of the tree into a canonical cophenetic matrix form suggests a simple and effective proposal distribution for selecting candidate trees close to the current tree in the chain. We illustrate the algorithm with restriction site data… 

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Phylogenetic Tree Construction Using Markov Chain Monte Carlo

TLDR
A Bayesian method based on Markov chain simulation to study the phylogenetic relationship in a group of DNA sequences that strikes a reasonable balance between the desire to move globally through the space of phylogenies and the need to make computationally feasible moves in areas of high probability.

Phylogenetic Inference for Binary Data on Dendograms Using Markov Chain Monte Carlo

Abstract Using a stochastic model for the evolution of discrete characters among a group of organisms, we derive a Markov chain that simulates a Bayesian posterior distribution on the space of

Markov chain Monte Carlo for the Bayesian analysis of evolutionary trees from aligned molecular sequences

TLDR
The challenging part is to approximate the posterior, and this is done by constructing a Markov chain having the posterior as its invariant distribution, following the approach of Mau, Newton, and Larget (1998).

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