Estimating the Size of Hidden Populations: A Bayesian Approach

Christian Tallberg

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.

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