To estimate parameters for demographic models described below, we used coalescent simulations to draw random ancestral recombination graphs (ARGs) conditional on specific demographic parameter values and compute the likelihood of observing the experimental data given these ARGs using custom programs.
After this step, we can start inserting the candidate subtree into the branches of the remaining tree and compute the likelihood score for each insertion.
From the 200 simulations we obtained a distribution of findings (0 indicating no significant connections, 1 that at least one connection had survived) at each threshold pair (significance and cluster-size) and computed the likelihood that a random data-set would yield a finding at the threshold (Fig. 2).
Parameters for mass error and peak intensity can be chosen individually for each dataset, and are required for computing the likelihood of the data.
Factored HMMs offer computational benefits when computing the likelihood of data.
Increasing the number of individuals is more problematic, as the time-complexity is cubic in the number of individuals, since every MCMC step involves computing the likelihood, and hence the inversion of a n× n matrix.
Initial work by Stamatakis and Ott (2008b) on methods for efficiently computing the likelihood on phylogenomic alignments with missing data focused on computing the likelihood and optimizing branch lengths on a single, fixed tree topology using pointer meshes.
Because the likelihood depends on the species tree topology and branch lengths, these must be specified in computing the likelihood.
Here, the parameter w is estimated by using a grid of values, i.e. w = 0.01, 0.03,..., 0.19, and computing the REML log-likelihood for each value.
