  Exponential random graph models are an important tool in the statistical
analysis of data. However, Bayesian parameter estimation for these models is
extremely challenging, since evaluation of the posterior distribution typically
involves the calculation of an intractable normalizing constant. This barrier
motivates the consideration of tractable approximations to the likelihood
function, such as the pseudolikelihood function, which offers an approach to
constructing such an approximation. Naive implementation of what we term a
pseudo-posterior resulting from replacing the likelihood function in the
posterior distribution by the pseudolikelihood is likely to give misleading
inferences. We provide practical guidelines to correct a sample from such a
pseudo-posterior distribution so that it is approximately distributed from the
target posterior distribution and discuss the computational and statistical
efficiency that result from this approach. We illustrate our methodology
through the analysis of real-world graphs. Comparisons against the approximate
exchange algorithm of Caimo and Friel (2011) are provided, followed by
concluding remarks.
