  In the following article we provide an exposition of exact computational
methods to perform parameter inference from partially observed network models.
In particular, we consider the duplication attachment (DA) model which has a
likelihood function that typically cannot be evaluated in any reasonable
computational time. We consider a number of importance sampling (IS) and
sequential Monte Carlo (SMC) methods for approximating the likelihood of the
network model for a fixed parameter value. It is well-known that for IS, the
relative variance of the likelihood estimate typically grows at an exponential
rate in the time parameter (here this is associated to the size of the
network): we prove that, under assumptions, the SMC method will have relative
variance which can grow only polynomially. In order to perform parameter
estimation, we develop particle Markov chain Monte Carlo (PMCMC) algorithms to
perform Bayesian inference. Such algorithms use the afore-mentioned SMC
algorithms within the transition dynamics. The approaches are illustrated
numerically.
