# 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…

## 517 Citations

### Phylogenetic Tree Construction Using Markov Chain Monte Carlo

- Biology
- 2000

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

- Mathematics
- 1997

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

- Biology
- 1999

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).

### Bayesian phylogenetic inference via Monte Carlo methods

- Biology
- 2012

The combinatorial sequential Monte Carlo (CSMC) method is proposed to generalize applications of SMC to non-clock tree inference based on the existence of a flexible partially ordered set (poset) structure, and it is presented in a level of generality directly applicable to many other combinatorsial spaces.

### Markov Chasin Monte Carlo Algorithms for the Bayesian Analysis of Phylogenetic Trees

- Computer Science
- 1999

We further develop the Bayesian framework for analyzing aligned nucleotide sequence data to reconstruct phylogenies, assess uncertainty in the reconstructions, and perform other statistical…

### Parallel algorithms for Bayesian phylogenetic inference

- Computer ScienceJ. Parallel Distributed Comput.
- 2003

### Assessing confidence in phylogenetic trees : bootstrap versus Markov chain Monte Carlo

- Mathematics
- 2002

Recent implementations of Bayesian approaches are one of the largest advances in phylogenetic tree estimation in the last 10 years. Markov chain Monte Carlo (MCMC) is used in these new approaches to…

### Markov chain Monte Carlo and its applications to phylogenetic tree construction

- Biology
- 2007

This thesis forms a novel Bayesian model for phylogenetic tree construction based on recent studies that incorporates known information about the evolutionary history of the species, referred to as the species phylogeny, in a statistically rigorous way and develops an inference algorithm based on a Markov chain Monte Carlo method in order to overcome the computational complexity inherent in the problem.

### A Variational Approach to Bayesian Phylogenetic Inference

- Computer ScienceArXiv
- 2022

This paper proposes combining subsplit Bayesian networks, an expressive graphical model for tree topology distributions, and a structured amortization of the branch lengths over tree topologies for a suitable variational family of distributions.

### Detecting recombination in 4-taxa DNA sequence alignments with Bayesian hidden Markov models and Markov chain Monte Carlo.

- Computer ScienceMolecular biology and evolution
- 2003

This article presents a statistical method for detecting recombination in DNA sequence alignments, which is based on combining two probabilistic graphical models: (1) a taxon graph (phylogenetic…

## References

SHOWING 1-10 OF 53 REFERENCES

### Phylogenetic Tree Construction Using Markov Chain Monte Carlo

- Biology
- 2000

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

- Mathematics
- 1997

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

- Biology
- 1999

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).

### Phylogenetic Tree Construction using Markov Chain

- Biology
- 1996

A Bayesian method based on Markov chain simulation to study the phylogenetic relationship in a group of DNA sequences and 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.

### Bayesian phylogenetic inference using DNA sequences: a Markov Chain Monte Carlo Method.

- BiologyMolecular biology and evolution
- 1997

An improved Bayesian method is presented for estimating phylogenetic trees using DNA sequence data, and the posterior probabilities of phylogenies are used to estimate the maximum posterior probability (MAP) tree, which has a probability of approximately 95%.

### Bayesian hypothesis testing of four-taxon topologies using molecular sequence data.

- BiologyBiometrics
- 1996

Bayesian inference under the principles of evolutionary parsimony is shown to be well calibrated with reasonable discriminating power for a wide range of realistic conditions, including conditions that violate the assumptions of evolutionary Parsimony.

### Markov Chains for Exploring Posterior Distributions

- Mathematics
- 1994

Several Markov chain methods are available for sampling from a posterior distribution. Two important examples are the Gibbs sampler and the Metropolis algorithm. In addition, several strategies are…

### MAXIMUM LIKELIHOOD INFERENCE OF PHYLOGENETIC TREES, WITH SPECIAL REFERENCE TO A POISSON PROCESS MODEL OF DNA SUBSTITUTION AND TO PARSIMONY ANALYSES

- Biology
- 1990

From the elucidation of implicit models underlying traditional "par- simony" and "compatibility" analyses, it is seen that Poisson process analysis gives a statistically consistent estimate of phylogeny, and that parsimony methods do indeed have a maximum likelihood foundation but give potentially incorrect estimates of phylogenies.

### Statistical inference of phylogenies

- Biology
- 1983

There are many unsolved problems, the most important of which is to persuade biologists to think of the problem of inferring phylogenies as being basically statistical, and to abandon deductive frameworks that are used as a justification for "parsimony" methods.

### Phylogenetic inference: linear invariants and maximum likelihood.

- BiologyBiometrics
- 1993

A new statistical method for inferring phylogenies, based on a likelihood ratio test, which shows that the validity of the method requires parameter constraints, but does not require that the evolutionary processes in differing sites be identical.