Amortized Bayesian Disease Mapping and Boundary Detection on Heterogeneous Spatial Graphs
Abstract
Spatial disease maps help public-health researchers identify geographic inequalities, but standard Bayesian smoothing can obscure localized disparities when neighboring communities have sharply different socioeconomic or behavioral profiles. Analysts therefore need to determine where smoothing should be interrupted and repeat that analysis as maps, adjacency structures, and outcomes change. We develop a covariate-informed Bayesian boundary model and an amortized posterior approximation trained across heterogeneous areal graphs. The model distinguishes local interruptions in smoothing from broader residual spatial dependence; the trained approximation handles maps with different numbers of regions. Simulations examine posterior calibration, boundary-probability recovery, replicated-data behavior, and MCSE-controlled agreement with prior-matched MCMC. In contrast to traditional approaches that analyze these data separately, we demonstrate the effectiveness of using a single trained deep learning network to analyze respiratory hospitalizations in Greater Glasgow; lung cancer incidence in California; and tracheal, bronchial, and lung cancer mortality in South Korea, comprising 58 to 241 regions. Selected boundary density is greatest in Glasgow and lowest in South Korea despite substantial residual spatial dependence in both, showing that local interruption and broader spatial persistence need not vary together. Across all three applications, edge-level boundary probabilities agree substantially with dataset-specific analyses, although posterior spread and thresholded boundary sets differ. These results support reusable Bayesian boundary analysis across the evaluated disease-map class and identify the validation needed before deployment to new applications.
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BibTeX
@misc{aiello2026amortized,
title = {{Amortized Bayesian Disease Mapping and Boundary Detection on Heterogeneous Spatial Graphs}},
author = {Luca Aiello and Sudipto Banerjee},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.30646},
eprint = {2609.30646},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.30646},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Amortized Bayesian Disease Mapping and Boundary Detection on Heterogeneous Spatial Graphs
AU - Luca Aiello
AU - Sudipto Banerjee
PY - 2026
DA - 2026/09/25
PB - arXiv
DO - 10.48550/arxiv.2609.30646
UR - https://arxiv.org/abs/2609.30646
AB - Spatial disease maps help public-health researchers identify geographic inequalities, but standard Bayesian smoothing can obscure localized disparities when neighboring communities have sharply different socioeconomic or behavioral profiles. Analysts therefore need to determine where smoothing should be interrupted and repeat that analysis as maps, adjacency structures, and outcomes change. We develop a covariate-informed Bayesian boundary model and an amortized posterior approximation trained across heterogeneous areal graphs. The model distinguishes local interruptions in smoothing from broader residual spatial dependence; the trained approximation handles maps with different numbers of regions. Simulations examine posterior calibration, boundary-probability recovery, replicated-data behavior, and MCSE-controlled agreement with prior-matched MCMC. In contrast to traditional approaches that analyze these data separately, we demonstrate the effectiveness of using a single trained deep learning network to analyze respiratory hospitalizations in Greater Glasgow; lung cancer incidence in California; and tracheal, bronchial, and lung cancer mortality in South Korea, comprising 58 to 241 regions. Selected boundary density is greatest in Glasgow and lowest in South Korea despite substantial residual spatial dependence in both, showing that local interruption and broader spatial persistence need not vary together. Across all three applications, edge-level boundary probabilities agree substantially with dataset-specific analyses, although posterior spread and thresholded boundary sets differ. These results support reusable Bayesian boundary analysis across the evaluated disease-map class and identify the validation needed before deployment to new applications.
ER -