Bayesian Spatial Framework for Quantifying Uncertainty in Labor Market Delineation

Abstract

Labor market delineation typically relies on deterministic regionalization algorithms that treat commuting flows as fixed inputs and produce a single optimal partition. These approaches obscure uncertainty in boundary placement and cannot distinguish stable labor market cores from transitional regions where affiliation is ambiguous. We develop a Bayesian framework for quantifying uncertainty in labor market boundaries by integrating hierarchical Poisson spatial modeling of commuting flows with cohesion-based regionalization. Commuting intensities are modeled using origin- and destination-specific socioeconomic covariates, distance, and conditional autoregressive (CAR) priors for spatially structured random effects. Posterior predictive commuting matrices are propagated through the Adaptive Simulated Annealing algorithm for Autonomous Labor Market Delineation, generating a distribution of regionalizations rather than a single partition. We introduce three complementary uncertainty measures: edge-level boundary probabilities, region-level membership stability, and local boundary pressure. Applied to Queensland, Australia commuting data (520 regions), the framework identifies approximately 10% of regions exhibit transitional behavior, with instability concentrated in peri-metropolitan growth corridors. Labor market boundaries emerge as probabilistic spatial equilibria characterized by stable cores and geographically localized transitional frontiers. The framework provides a rigorous basis for evaluating boundary robustness, directing expert review boundary delineation, and identifying areas of structural instability for regional policy and infrastructure planning.