The U.S. Decennial Census serves as the foundation for many high-profile policy decision-making processes, including federal funding allocation and redistricting. In 2020, the Census Bureau adopted differential privacy to protect the confidentiality of individual responses through a disclosure avoidance system that injects noise into census data tabulations. The Bureau subsequently posed an open question: Could sharper privacy guarantees be obtained for the 2020 U.S. Census compared to their published guarantees, or equivalently, had the nominal privacy budgets been fully utilized? In this paper, we affirmatively address this open problem by demonstrating that between 8.50% and 13.76% of the privacy budget for the 2020 U.S. Census remains unused for each of the eight geographical levels, from the national level down to the block level. This finding is made possible through our precise tracking of privacy losses using $f$-differential privacy, applied to the composition of private queries across various geographical levels. Our analysis indicates that the Census Bureau introduced unnecessarily high levels of injected noise to achieve the claimed privacy guarantee for the 2020 U.S. Census. Consequently, our results enable the Bureau to reduce noise variances by 15.08% to 24.82% while maintaining the same privacy budget for each geographical level, thereby enhancing the accuracy of privatized census statistics. We empirically demonstrate that reducing noise injection into census statistics mitigates distortion caused by privacy constraints in downstream applications of private census data, illustrated through a study examining the relationship between earnings and education.

Population synthesis consists of generating synthetic but realistic representations of a target population of micro-agents for the purpose of behavioral modeling and simulation. We introduce a new framework based on copulas to generate synthetic data for a target population of which only the empirical marginal distributions are known by using a sample from another population sharing similar marginal dependencies. This makes it possible to include a spatial component in the generation of population synthesis and to combine various sources of information to obtain more realistic population generators. Specifically, we normalize the data and treat them as realizations of a given copula, and train a generative model on the normalized data before injecting the information on the marginals. We compare the copulas framework to IPF and to modern probabilistic approaches such as Bayesian networks, variational auto-encoders, and generative adversarial networks. We also illustrate on American Community Survey data that the method proposed allows to study the structure of the data at different geographical levels in a way that is robust to the peculiarities of the marginal distributions.