MrBayes is a program for the Bayesian estimation of phylogeny. Bayesian inference of phylogeny is based upon a quantity called the posterior probability distribution of trees, which is the probability of a tree conditioned on the observations. The conditioning is accomplished using Bayes’s theorem. The posterior probability distribution of trees is impossible to calculate analytically; instead, MrBayes uses a simulation technique called Markov chain Monte Carlo (or MCMC) to approximate the posterior probabilities of trees.
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MrBayes 3.2: efficient Bayesian phylogenetic inference and model choice across a large model space.
Ronquist F, Teslenko M, van der Mark P, Ayres DL, Darling A, Höhna S, Larget B, Liu L, Suchard MA, Huelsenbeck JP.
Syst Biol. 2012 May;61(3):539-42. doi: 10.1093/sysbio/sys029.
Ronquist F, Huelsenbeck JP.
MrBayes 3: Bayesian phylogenetic inference under mixed models.
Bioinformatics. 2003 Aug 12;19(12):1572-4.