Bayesian Inference for Spatially‐Temporally Misaligned Data Using Predictive Stacking

Air pollution remains a major environmental risk factor that is often associated with adverse health outcomes. However, quantifying and evaluating its effects on human health is challenging due to the complex nature of exposure data. Recent technological advances have led to the collection of various indicators of air pollution at increasingly high spatial‐temporal resolutions (e.g., daily averages of pollutant levels at spatial locations referenced by latitude‐longitude). However, health outcomes are typically aggregated over several spatial‐temporal coordinates (e.g., annual prevalence for a county) to comply with survey regulations. This article develops a Bayesian hierarchical model to analyze such spatially‐temporally misaligned exposure and health outcome data. We develop Bayesian predictive stacking for spatially and temporally misaligned data to optimally combine inference from multiple predictive spatial‐temporal models. Stacking allows us to avoid iterative estimation algorithms such as Markov chain Monte Carlo that struggle due to convergence issues inflicted by the presence of weakly identified parameters. We apply our proposed method to study the effects of ozone on asthma in the state of California.