MrBayes is a program for doing Bayesian phylogenetic analysis including phylogenetic reconstruction. Bayesian inference of phylogeny is based on 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 often impossible to calculate analytically; instead, MrBayes uses a simulation technique called Markov Chain Monte Carlo (MCMC) to approximate the posterior probabilities of trees.
Huelsenbeck JP, Ronquist F., MRBAYES: Bayesian inference of phylogenetic trees,Bioinformatics. 2001 Aug;17(8):754-5.
Fredrik Ronquist and Andrew R. Deans, Bayesian Phylogenetics and Its Influence on Insect Systematics, Annual Review of Entomology
Vol. 55: 189-206 (Volume publication date January 2010),First published online as a Review in Advance on October 5, 2009,DOI: 10.1146/annurev.ento.54.110807.090529