University of Washington - Department of Statistics
Exponential-family random graph model (ERGM) has been widely applied in the fields of social network analysis, genetics (e.g. protein interaction networks), information theory etc. Because of the intractability of the likelihood function, Markov Chain Monte-Carlo (MCMC) approximation is typically applied to obtain maximum likelihood estimators (Geyer and Thompson 1992). However, ERGMs still suffer from inferential degeneracy and computational deficiency. In this talk, we present the Bayesian inference to ERGM. Simulation studies are carried out to illustrate how Bayesian analysis resolves computational degeneracy and bias-reduction problems. We particularly are interested in conjugate analysis ERGM. We are able to show the superiority of conjugate prior over non-informative priors. Various efficient MCMC algorithms are studied and compared.
Only few studies address model selection problems for ERGM. In this talk, we propose a novel systematic procedure to conduct likelihood ratio tests to compare ERG models. Given two sets of models, we evaluate the likelihood ratio statistic, explore its sampling distribution and calculate the Monte-Carlo p-values for hypothesis testing. In addition, we develop a numerical algorithm to estimate the Bayes factor for given models. Finally, likelihood ratio tests and Bayesian model selection are tested and compared using real social network data.
Variational representation of exponential families and its application on parameter estimation of ERGM will be discussed at the end.