Copula Gaussian graphical modelling of biological networks and Bayesian inference of model parameters

Understanding complex biological networks enable us to better understand the systems’ diseases such as cancers and heart attacks, and to produce drug targets which is one of the major research questions under the personalized medicine. But the description of these complexities is challenging since the associated data are very sparse, high dimensional and seriously correlated. The copula Gaussian graphical model (CGGM), which depends on the representation of the multivariate normal distribution via marginals and a copula term, is one of the successful modelling approaches to present such type of datasets. In this study, we apply CGGM in modelling steady-state activations of biological networks and make inference of model parameters under Bayesian settings. We suggest the reversible jump Markov chain Monte Carlo (RJMCMC) algorithm to estimate plausible interactions between the systems’ elements which are proteins or genes. We also generate the open-source R codes of RJMCMC for CGGM under different dimensional networks. In the application, we use real datasets and evaluate the accuracy of estimates via F1-score. From the results, we observe that CGGM with RJMCMC is successful in the presentation of real and complex systems with higher accuracy and can be a promising approach to understand biological networks and diseases.