Bayesian Estimation of Blockstructures from Snowball Samples

Christian Tallberg

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.

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