- Maximum likelihood attempts to find the phylogenetic tree and evolutionary model that have the highest probability of producing the observed sequence data. - The likelihood of observing the data depends on the evolutionary model used and can change if the model changes, even if the data remains the same. - Markov chain Monte Carlo methods are used in Bayesian inference to approximate the posterior probabilities of trees since the exact joint probabilities cannot be calculated analytically. Trees are sampled from their posterior probability distribution to make inferences.