Estimation with link: Tracing sampling designs: A Bayesian approach

In link-tracing designs, social links are followed from one respondent to another to obtain the sample. For hidden and hard-to-access human populations, such sampling designs are often the only practical way to obtain a sample large enough for an effective study. In this paper, we propose a Bayesian approach for the estimation problem. For studies using link-tracing designs, prior information may be available on the characteristics that one wants to estimate. Using this information effectively via a Bayesian approach should yield better estimators. When the available information is vague, one can use noninformative priors and conduct a sensitivity analysis. In our example we found that the estimators were not sensitive to the specified priors. It is important to note that, under the Bayesian setup, obtaining interval estimates to assess the accuracy of the estimators can be done without much added difficulty. By contrast, such tasks are difficult to perform using the classical approach. In general, a Bayesian analysis yields one distribution (the posterior distribution) for the unknown parameters, and from this a vast number of questions can be answered simultaneously.