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This paper explores the concepts and computational methods used tomeasure spatial inequality, emphasizing a reproducible approach thatsocial scientists can apply to their research. The analysis focuses ongeographic income disparities at the sub-national level, using Mexico asa case study. By examining various a-spatial and spatially explicitapproaches, the paper highlights the complexities of measuringinequality across places and over time. The discussion includes a reviewof traditional inequality measures and introduces spatial decompositionmethods that account for the geographical distribution of income. Thefindings underscore the importance of integrating spatial considerationsinto inequality analysis to better understand the patterns and driversof regional disparities, thereby informing more effective and equitablepolicy interventions. 

ABSTRACT GIS and GIScience education have continually evolved over the past three decades, responding to technological advances and societal issues. Today, the content and context in which GIScience is taught continue to be impacted by these disruptions, notably from technology through artificial intelligence (AI) and society through the myriad environmental and social challenges facing the planet. These disruptions create a new landscape for training within the discipline that is affecting not onlywhatis taught in GIScience courses but alsowhois taught,whyit is being taught, andhowit is taught. The aim of this paper is to structure a direction for developing and delivering GIScience education that, amid these disruptions, can generate a capable workforce and the next generation of leaders for the discipline. We present a framework for understanding the various emphases of GIScience education and use it to discuss how the content, audience, and purpose are changing. We then discuss how pedagogical strategies and practices can change how GIScience concepts and skills are taught to train more creative, inclusive, and empathetic learners. Specifically, we focus on how GIScience pedagogy should (1) center on problem‐based learning, (2) be open and accelerate open science, and (3) cultivate ethical reasoning and practices. We conclude with remarks on how the principles of GIScience education can extend beyond disciplinary boundaries for holistic spatial training across academia. 

The process of regionalization involves clustering a set of spatial areas into spatially contiguous regions. Given the NP-hard nature of regionalization problems, all existing algorithms yield approximate solutions. To ascertain the quality of these approximations, it is crucial for domain experts to obtain statistically significant evidence on optimizing the objective function, in comparison to a random reference distribution derived from all potential sample solutions. In this paper, we propose a novel spatial regionalization problem, denoted as SISR (Statistical Inference for Spatial Regionalization), which generates random sample solutions with a predetermined region cardinality. The driving motivation behind SISR is to conduct statistical inference on any given regionalization scheme. To address SISR, we present a parallel technique named PRRP (P-Regionalization through Recursive Partitioning). PRRP operates over three phases: the region-growing phase constructs initial regions with a predetermined region cardinality, while the region merging and region-splitting phases ensure the spatial contiguity of unassigned areas, allowing for the growth of subsequent regions with predetermined cardinalities. An extensive evaluation shows the effectiveness of PRRP using various real datasets. 

Abstract American Community Survey (ACS) data have become the workhorse for the empirical analysis of segregation in the U.S.A. during the past decade. The increased frequency the ACS offers over the 10-year Census, which is the main reason for its popularity, comes with an increased level of uncertainty in the published estimates due to the reduced sampling ratio of ACS (1:40 households) relative to the Census (1:6 households). This paper introduces a new approach to integrate ACS data uncertainty into the analysis of segregation. Our method relies on variance replicate estimates for the 5-year ACS and advances over existing approaches by explicitly taking into account the covariance between ACS estimates when developing sampling distributions for segregation indices. We illustrate our approach with a study of comparative segregation dynamics for 29 metropolitan statistical areas in California, using the 2010–2014 and 2015–2019. Our methods yield different results than the simulation technique described by Napierala and Denton (Demography 54(1):285–309, 2017). Taking the ACS estimate covariance into account yields larger error margins than those generated with the simulated approach when the number of census tracts is large and minority percentage is low, and the converse is true when the number of census tracts is small and minority percentage is high.