Sampling from a hidden population is a well known problem in Epidemiology. Consider, for example, the task of estimating the prevalence of HIV among users of intravenous drugs. In this setting, sampling mechanisms like Respondent-Driven Sampling (RDS) allows the researcher to examine such populations by taking advantage of the social network structure. In the case of the drug abusers, edges in the network encode the act of sharing needles.
We proposed a modelling strategy that allows us to perform inference on a population quantity Q (for instance, the prevalence of HIV among users of intravenous drugs) while taking into account the most relevant sources of uncertainty. One of these sources of uncertainty is the sampling mechanism itself: We prove that RDS is non-ignorable and show how this should be incorporated in the likelihood. Our modelling approach is modular with respect to the model specification and computation of the posterior.