Bayesian inference in phylogeny generates a posterior distribution for a parameter, composed of a phylogenetic tree and a model of evolution, based on the prior for that parameter and the likelihood of the data, generated by a multiple alignment. The Bayesian approach has become more popular due to advances in computational machinery, especially, Markov chain Monte Carlo algorithms. Bayesian inference has a number of applications in molecular phylogenetics, for example, estimation of species phylogeny and species divergence times.
Read more about Bayesian Inference In Phylogeny: Basic Bayesian Theory, The LOCAL Algorithm of Larget and Simon, Metropolis-coupled MCMC (Geyer)
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“Rules and particular inferences alike are justified by being brought into agreement with each other. A rule is amended if it yields an inference we are unwilling to accept; an inference is rejected if it violates a rule we are unwilling to amend. The process of justification is the delicate one of making mutual adjustments between rules and accepted inferences; and in the agreement achieved lies the only justification needed for either.”
—Nelson Goodman (b. 1906)