Maximum Likelihood

Given a tree, we often wish to have a statistical measure of how well it describes our data. As we have seen earlier in the course, we can use the likelihood score to estimate our hypothesis, which is in this case a phylogenetic tree T. For a set of species with observed values M, we would choose the tree that maximizes P(M|T). In the following section, we shall assume that the tree topology is known, and show how to find the optimal branch lengths. To this end, we will first demonstrate how to calculate the likelihood of a tree efficiently. We will not discuss the issue of searching among tree topologies, which suffers from the same difficulties we mentioned in the previous sections, although is not proven to be NP-complete.