Spatial Boundary Detection for Areal Counts

A statistical test on the local effects of spatially structured variance

“…Another closely related research field is concerned with integrating spatial heterogeneity with quantitative models. The respective approaches include the following: hierarchical and Bayesian concepts (Lee and Mitchell 2012, Anderson et al 2014, Hanson et al 2015, geostatistical techniques (Garrigues et al 2006, Goovaerts 2008, Hu et al 2015, extensions to global spatial regression methods (Anselin 2001), and the local geographically-weighted regression approach (Fotheringham et al 1996, Brunsdon et al 1998.…”

Spatial non-parametric Bayesian clustered coefficients

“…Recent advancements in methods for spatial boundary detection have focused on model-based approaches which focus on probabilistic uncertainty quantification 3 , 4 . An exemplar paper is by Lee 5 , who employs stochastic models for adjacency matrices in order to identify edges between regions with significant differences in health outcomes.…”

Discussion of “Optimal Test Procedures for Multiple Hypotheses Controlling the Familywise Expected Loss” by Willi Maurer, Frank Bretz, and Xiaolei Xun

“…An immediate concern is that these spatial random effects are typically endowed with a multivariate Gaussian distribution using Markov random fields or Gaussian processes and, being continuous distributions, the posterior probability of any two random effects being equal will be zero. Modeling spatial random effects with discrete jumps, step changes, and discontinuities have been addressed in diverse settings (see, e.g., Gao et al, 2022;Hanson et al, 2015;Li et al, 2012Li et al, , 2015Rushworth et al, 2017;Santafé et al, 2021).…”