Bayesian inference in phylogeny
| Classification | Evolutionary biology |
|---|---|
| Subclassification | Molecular phylogenetics |
| Optimally search criteria | Bayesian inference |
Bayesian inference of phylogeny uses a likelihood function to create a quantity called the posterior probability of trees using a model of evolution, based on some prior probabilities, producing the most likely phylogenetic tree for the given data. The Bayesian approach has become popular due to advances in computing speeds and the integration of Markov chain Monte Carlo (MCMC) algorithms. Bayesian inference has a number of applications in molecular phylogenetics and systematics.
Bayesian inference refers to a probabilistic method developed by Reverend Thomas Bayes based on Bayes' theorem. Published posthumously in 1763 it was the first expression of inverse probability and the basis of Bayesian inference. Independently, unaware of Bayes work, Pierre-Simon Laplace developed Bayes' theorem in 1774.
Bayesian inference was widely used until 1900s when there was a shift to frequentist inference, mainly due to computational limitations. Based on Bayes' theorem, the bayesian approach combines the prior probability of a tree P(A) with the likelihood of the data (B) to produce a posterior probability distribution on trees P(A|B). The posterior probability of a tree will indicate the probability of the tree to be correct, being the tree with the highest posterior probability the one chosen to represent best a phylogeny. It was the introduction of MCMC methods by Nicolas Metropolis in 1953 that revolutionized Bayesian Inference and by the 1990s became a widely used method amongst phylogeneticists. Some of the advantages over traditional maximum parsimony and maximum likelihood methods are the possibility of account for the phylogenetic uncertainty, use of prior information and incorporation of complex models of evolution that limited computational analyses for traditional methods. Although overcoming complex analytical operations the posterior probability still involves a summation over all trees and, for each tree, integration over all possible combinations of substitution model parameter values and branch lengths.
MCMC methods can be described in three steps: first using a stochastic mechanism a new state for the Markov chain is proposed. Secondly, the probability of this new state to be correct is calculated. Thirdly, a new random variable (0,1) is proposed. If this new value is less than the acceptance probability the new state is accepted and the state of the chain is updated. This process is run for either thousands or millions of times. The amount of time a single tree is visited during the course of the chain is just a valid approximation of its posterior probability. Some of the most common algorithms used in MCMC methods include the Metropolis-Hastings algorithms, the Metropolis-Coupling MCMC (MC³) and the LOCAL algorithm of Larget and Simon.
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