Causal Inference for Geostatistical Data Using an INLA-based Spatial Propensity Score

In this paper, we propose a Bayesian approach for spatial causal inference based on combining spatial propensity scoring with Integrated Nested Laplace Approximation. The method models both local and spillover exposure effects via multiple likelihoods and treats counterfactuals as missing data, allowing inference also for non-Gaussian outcomes. We validated the proposed method through simulations and an application to U.S. county-level cancer data, demonstrating the critical importance of properly accounting for spatial dependence when drawing causal conclusions from geostatistical data. Our results show that the proposed method achieves MCMC-comparable accuracy with substantially reduced computational time.