Composite Likelihood Adjustment in Bayesian Inference for Estimating Species Tree Parameters Under the Multispecies Coalescent

Composite likelihood methods have long been used in biology to facilitate efficient computation for the high-dimensional, dependent structures commonly present in genetic data. In species-level phylogenetic inference under the multispecies coalescent model, the full likelihood is computationally intractable, while the composite likelihood can be efficiently computed. However, using the composite likelihood instead of the full likelihood in Bayesian inference involves repeated use of data, resulting in overly concentrated posteriors. We develop a method that incorporates an adjustment to the composite likelihood in a Bayesian framework to adjust the approximated posterior distributions so that credible intervals achieve the correct coverage. Both simulated and empirical data are used to show that our method compares favorably with existing methods with respect to both computation time and accuracy.