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. Utilizing American Community Survey data, we propose a Bayesian model for boundary detection based on income distributions. The model identifies areas with significant income disparities, offering actionable insights for policymakers to address social and economic inequalities. Our approach formalized as a Bayesian structural learning framework, models areal densities through finite mixture models. 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 distributions in the greater Los Angeles area. We identify several boundaries in the income distributions which can be explained in light of other social dynamics such as crime rates and healthcare, showing the usefulness of such an analysis to policymakers.

翻译：关于大都市未来发展的近期讨论凸显了社会公平的关键作用，这一趋势受到人口结构与经济变化的双重驱动。更平等的政策能够促进城市经济成功并维护社会稳定。本研究聚焦于识别美国最具多元性却最不平等的地区之一——大洛杉矶地区内具有显著社会经济水平差异的大都市区域。基于美国社区调查数据，我们提出一种基于收入分布的贝叶斯边界检测模型。该模型能够识别收入显著失衡的区域，为政策制定者解决社会经济不平等问题提供可操作洞见。我们的方法被形式化为贝叶斯结构学习框架，通过有限混合模型对区域密度进行建模，并借助跨维度马尔可夫链蒙特卡洛采样器实现高效后验计算。该方法经广泛模拟验证后，被应用于大洛杉矶地区的收入分布分析。我们识别出收入分布中的若干边界，这些边界可结合犯罪率、医疗服务等社会动态因素加以阐释，充分展示了此类分析对政策制定者的实用价值。