Indirect surveys have been used for decades by epidemiologists and social scientists to estimate the size of sub-populations within social networks. In these surveys, respondents provide information about their social connections, making them particularly useful for monitoring hard-to-reach or sensitive populations, such as disaster casualties, drug use prevalence, or the spread of infectious diseases. These indirect responses, known as Aggregated Relational Data (ARD), are analyzed using various statistical methods collectively referred to as the Network Scale-Up Method (NSUM). However, to the best of our knowledge, no analytical bounds have been established for the estimation errors that may occur with NSUM.

In this seminar, we first focus on two popular NSUM estimators, demonstrating that in the worst-case scenario, the estimation error can be a factor of Ω(√n) away from the actual sub-population size, where n is the number of nodes in the network. Additionally, we prove that for random social networks, a small constant error factor can be achieved with high probability using logarithmic-sized samples.

We then focus to the application of indirect online surveys for continuous data collection. While NSUM can be applied by analyzing data independently at each time point, this approach overlooks the potential benefits of leveraging temporal data. Instead, we propose an approach that uses ARD collected over time, proving that indirect surveys can provide more accurate estimates of sub-population trends compared to direct surveys. Additionally, we identify appropriate methods for temporal aggregation to further enhance the accuracy of these estimates.