Bayesian inference of exponential random graph models under measurement errors

While the impact of measurement errors inherent in network data has been widely recognized, relatively little work has been done to solve the problem mainly due to the complex dependence nature of network data. In this paper, we propose a Bayesian inference framework for summary statistics of the true underlying network, based on the network observed with measurement errors. To the best of our knowledge, this paper is the first to deal with measurement errors in the network data analysis in a Bayesian framework. We construct a Gibbs sampler to iteratively draw underlying true networks and model parameters. We incorporate the exponential random graph model to serve as the likelihood function, and use the exchange algorithm to draw model parameters. Simulation results show that using our inference framework, the impact of measurement errors has been reduced significantly.