The snowball sampling procedure is considered to estimate the size of
small hidden populations. Previous work in this area have been based on
models where the probability of relations is the same across all pairs
of members in the network.\ Here, we use a more general blockmodel which
allows a richer probabilistic structure. Bayesian methods are employed
and the posterior distribution of the size of the population is easily
computed analytically if the block labels are known. If the block labels
are unknown or latent, the posterior distribution is computed by the Gibbs
sampler algorithm. The Gibbs sampler also provides us with the posterior
distributions of other model parameters without any additional difficulty.
Keywords: Bayesian analysis; Hidden population; Network sampling;
Random graphs; Stochastic blockmodels.