🤖 AI Summary
This study addresses the challenge of quantifying population segregation by proposing a general measurement framework based on convex functions over the probability simplex. Methodologically, it leverages Jensen’s inequality to define segregation as the discrepancy between local and global diversity, thereby constructing Jensen-information-based measures. To incorporate spatial structure, three strategies are introduced: spatial smoothing, aggregation, and local Jensen information. By integrating convex optimization with spatial statistics theory, this work establishes a comprehensive mathematical system for measuring segregation. Computational examples validate the effectiveness of various spatial modeling approaches. Ultimately, this research provides a unified theoretical foundation for quantifying the interplay between population attributes and spatial separation.
📝 Abstract
The problem of segregation measurement is to quantitatively describe the interaction of a population's attributes (such as race, ethnicity, education level, or income) with a separating distinction (such as organizational rank, school district, or spatial location). This primarily expository article gives an opinionated tour of one mathematical approach to measuring segregation. We begin with some basic intuitions about diversity and unify these through the framework of convex functions on the probability simplex. Formalizing segregation as a local-to-global comparison of diversity measures, resulting in the general class of Jensen informations as segregation measurements. We describe and computationally illustrate three ways to incorporate spatial structure into segregation measurements: spatial smoothing, aggregation, and local Jensen information. We close with several suggestions for future work.