1. BNFO 602 Phylogenetics
Usman Roshan

2. Maximum Likelihood D = data, M = model Bayes rule
P(M|D) = P(D|M)P(M) / P(D)
P(M|D) is the posterior probability
P(D|M) is the likelihood
P(M) is the prior probability on the model
By rewriting P(D) we get
= P(D|M)P(M) / ∑M P(D|M)P(M)
which implies that
P(M|D) is proportional to P(D|M)P(M)
Note that by assuming uniform priors
P(M|D) = P(D|M)1/k / ∑M P(D|M)1/k

3. Maximum Likelihood Data (input) is the alignment Model consists of
the tree with branch lengths and leaves labeled with the DNA sequences in the data (input)
a DNA sequence evolution model (such as Jukes Cantor)
How do we compute the likelihood P(D|T) of the tree below?

4. Which of the two trees below have the higher likelihood?

5. Maximum Likelihood
ML problem: Under a fixed model find the tree with branch lengths and internal nodes that has the highest likelihood.
Very large search space
NP-hard
Sub-problems
What is the likelihood of a tree with branch lengths and internal nodes?
Linear time solution
What if no internal nodes are given?
Felsenstein’s algorithm gives linear time solution
What if no branch lengths are given?
We use gradient descent

6. Maximum Likelihood Comparison to MP:
Both are NP-hard
For fixed tree it takes polynomial time to find the parsimony score
For fixed tree is is NP-hard to find the likelihood score
Similar local search heuristics as MP