A Bayesian phylogenetic hidden Markov model for B cell receptor sequence analysis
Fig 6
A graphical model representation of our phylo-HMM for an example alignment with m = 3 sequences and n = 3 sites.
The τ, t, π, and e nodes represent the 4-tip unrooted tree topology, the associated 5 branch lengths, the GTR exchangeability rates, and GTR equilibrium base frequencies, respectively. The parameter α denotes the gamma shape parameter associated with the K-class discrete gamma distribution, which is used to model phylogenetic rate variation among sites; r symbolizes the vector of K discrete rates that is deterministically induced by α. The set of nodes defines the rates that are drawn from r at each particular site. The
“hidden state” node collection represents the Markov process that stochastically generates the naive sequence in our phylo-HMM. The node sets
and
denote the internal nodes of τ excluding the naive sequence Ynaive and the observed MSA, respectively. We draw plates around the
and D(j) node sets for j ∈ {1, 2, 3} to indicate that any directed edges touching a plate apply to all nodes in the plate (except for edges that originate from t, which apply element-wise to the nodes in the plate).