title: Bayesian Analysis for Exponential Random Graph Models Using the Adaptive Exchange Sampler.
abstract: Exponential random graph models have been widely used in social network analysis. However, these models are extremely difficult to handle from a statistical viewpoint, because of the intractable normalizing constant and model degeneracy. In this paper, we consider a fully Bayesian analysis for exponential random graph models using the adaptive exchange sampler, which solves the intractable normalizing constant and model degeneracy issues encountered in Markov chain Monte Carlo (MCMC) simulations. The adaptive exchange sampler can be viewed as a MCMC extension of the exchange algorithm, and it generates auxiliary networks via an importance sampling procedure from an auxiliary Markov chain running in parallel. The convergence of this algorithm is established under mild conditions. The adaptive exchange sampler is illustrated using a few social networks, including the Florentine business network, molecule synthetic network, and dolphins network. The results indicate that the adaptive exchange algorithm can produce more accurate estimates than approximate exchange algorithms, while maintaining the same computational efficiency.
authors.affiliation: Department of Biostatistics, The University of Texas MD Anderson Cancer Center, Houston, TX 77030-4009, USA.
authors.forename: Ick Hoon
authors.initials: IH
authors.lastname: Jin
authors.affiliation: Department of Biostatistics, The University of Texas MD Anderson Cancer Center, Houston, TX 77030-4009, USA.
authors.forename: Ying
authors.initials: Y
authors.lastname: Yuan
authors.affiliation: Department of Statistics, Texas A&M University, College Station, TX, 77843-3143, USA.
authors.forename: Faming
authors.initials: F
authors.lastname: Liang
keywords: Adaptive Markov chain Monte Carlo; Exchange Algorithm; Exponential Random Graph Model; Social Network