Bayesian nonparametric boundary detection for income areal data

Abstract: Recent discussions on the future of metropolitan cities underscore the pivotal role of (social) equity, driven by demographic and economic trends. More equal policies can foster and contribute to a city's economic success and social stability. In this work, we focus on identifying metropolitan areas with distinct economic and social levels in the greater Los Angeles area, one of the most diverse yet unequal areas in the United States. Utilising American Community Survey data, we propose a Bayesian model for boundary detection based on areal income distributions. The model identifies areas with significant income disparities, offering actionable insights for policymakers to address social and economic inequalities. We have multiple observations (i.e., personal income of survey respondents) for each area, and our approach, formalised as a Bayesian structural learning framework, models areal densities through mixtures of finite mixtures. We address boundary detection by identifying boundaries for which the associated geographically contiguous areal densities are estimated as being very different without resorting to dissimilarity metrics or covariates. Efficient posterior computation is facilitated by a transdimensional Markov Chain Monte Carlo sampler. The methodology is validated via extensive simulations and applied to the income data in the greater Los Angeles area. We identify several boundaries in the income distributions, which can be explained ex-post in terms of the percentage of the population without health insurance, though not in terms of the total number of crimes, showing the usefulness of such an analysis to policymakers.