Bayesian inference for duplication-mutation with complementarity network models

We observe an undirected graph G without multiple edges and self-loops, which is to represent a protein-protein interaction (PPI) network. We assume that G evolved under the duplication-mutation with complementarity (DMC) model from a seed graph, G0, and we also observe the binary forest Γ that represents the duplication history of G. A posterior density for the DMC model parameters is established, and we outline a sampling strategy by which one can perform Bayesian inference; that sampling strategy employs a particle marginal Metropolis-Hastings (PMMH) algorithm. We test our methodology on numerical examples to demonstrate a high accuracy and precision in the inference of the DMC model's mutation and homodimerization parameters.