Spatial Disease Mapping and Disparity Detection Using Generative AI: An Amortized Bayesian Learning Framework
We introduce an amortized Bayesian framework for spatial boundary detection that generalizes posterior inference across areal graphs with varying numbers of regions and diverse adjacency structures. The underlying model couples a Poisson count likelihood with a covariate-driven rule to interrupt smoothing across dissimilar neighboring areas, utilizing a directed acyclic graph autoregressive (DAGAR) prior to capture residual spatial dependence. To approximate the target posterior distribution, a neural engine is trained on simulated maps: a permutation-invariant summary network encodes graph-aware representations of the observed counts, offsets, covariates, and adjacency matrices, while a conditional normalizing flow generates the approximate posterior draws. Simulation studies demonstrate accurate parameter recovery, near-nominal interval coverage, well-calibrated posterior predictive behavior, and informative posterior boundary probabilities. Benchmarking against Markov chain Monte Carlo (MCMC) confirms close agreement regarding primary boundary evidence, and an ablation study validates the inclusion of model-guided graph summaries. Finally, applications to Glasgow respiratory disease and California lung cancer data demonstrate that a single trained neural engine can be seamlessly deployed across real-world maps with distinct graph structures, yielding boundary conclusions consistent with established localized smoothing analyses.