2025 Theses Doctoral

Statistical Methods for Understanding Social Issues

Bradshaw, Casey

The modern-day abundance of both data and computational resources has expanded the potential for statistical methods to improve our understanding of social phenomena. Such insights can also serve as a basis for policy decisions and resource allocation. This thesis explores pragmatic approaches to statistical inference in select applications related to social issues.

We begin by considering underreporting of sexual assault on college campuses. Because many instances of sexual assault are never reported to authorities, the number of reported assaults does not fully reflect the true total number of assaults that occurred, and could arise from many combinations of reporting rate and true incidence. We estimate these quantities via a hierarchical Bayesian model of the reported data, drawing prior information from national crime statistics to help distinguish between reporting rates and incidence.

Next, we consider the task of detecting election interference, focusing on Ghana’s 2020 presidential election. Using locally-aggregated vote tabulation data, we construct a randomization test to screen for potential ballot box stuffing. After identifying regions with suspicious results, we estimate alternative vote totals under a counterfactual scenario with no election interference.

Next we turn our attention to synthetic control methods for causal inference. Using a motivating example of estimating the effects of exogenous economic shocks on support for political incumbents, we propose methods for leveraging shared information across multiple related studies.

Finally, we address the issue of data privacy. Motivated by the need to balance the utility of data analysis with protection of individuals’ privacy, we develop randomized optimization algorithms for differentially private statistical inference. These procedures allow the construction of private confidence regions, and employ a bias correction that improves empirical performance in small samples.