A phylogenetic tree describes ancestral relationships. In a probabilistic graphical model on a rooted tree, latent variables at ancestral vertices are inferred from observations at leaves using belief propagation.
The Felsenstein pruning algorithm computes a site likelihood function by sum-product belief propagation from leaves to root. For a finite-state Markov kernel , the subtree likelihood function obeys , with observed-state indicators at leaves. Summing against the root probability distribution gives the site likelihood function. An outward pass gives edge posterior probabilities and expected transition counts for the expectation-maximization algorithm.
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Phylogenetics is a field of biology that studies the evolutionary relationships among various biological species or entities based on their physical and genetic characteristics. This discipline primarily uses the concept of a phylogenetic tree, a diagram that represents the evolutionary pathways and relationships among different organisms, showing how they diverged from common ancestors over time.
