The problem of estimating the size of hidden populations is considered.
A practical design to obtain efficient estimators is snowball sampling
which allows units to provide information not only about themselves but
also about other units. In classical approaches inferences about the model
are based on asymptotic theory, and accuracy of confidence statements
is questionable for small sample sizes. We employ Bayesian methods enabling
exact finite sample inference in terms of whole distributions of the unknown
parameters given the observed data. Often, prior information on the model
parameters is available. The Bayesian analysis enjoys the advantage of
the possibility to implement this information into the analysis which,
if properly used, should improve the estimators. Simulation results are
provided where the Bayesian estimator is compared to frequentist competitors.
Applications of our proposed model are illustrated with analysis to three
studies of hard drug use.
Keywords: Bayesian analysis; Network sampling; Random graphs.