Jens Malmros: Random walks and respondent-driven sampling on directed networks

Respondent-driven sampling (RDS) is a commonly used method when sampling from hidden populations, e.g. injecting drug users, homosexual males and sex workers, which due to social stigmatization and/or legal difficulties arising from their behavior often are hard to reach by conventional methods. RDS utilizes the social network of the population by recruiting participants through a snowball-like mechanism and also comprises a mathematical model that facilitates unbiased population estimates given that the actual RDS process is approximated by a random walk on the network. One key assumption in the random walk model, not likely to be fulfilled, is that the social network of the population is undirected. Therefore it is of interest to expand the model, and consequently RDS estimation, to directed networks. In this work, we try to do so by developing a random walk framework for directed networks. We suggest estimators for the stationary distribution that can be used for RDS estimation on directed networks both for the theoretical case where the full directed degree is observed as well as for the situation when only out-degree is observed.