Coal burning power plants are a frequent target of regulatory programmes because of their emission of chemicals that are known precursors to the formation of ambient particulate air pollution. Health impact assessments of emissions from coal power plants typically rely on assumed causal relationships between emissions, ambient pollution and health, many of which have never been empirically verified. We offer a novel statistical evaluation of some of these presumed causal relationships, integrating the formality of causal inference methods with repurposed tools from atmospheric science to accommodate the central challenge of long-range pollution transport of emissions from power plants to exposed populations. The statistical approach follows recent work on Bayesian methods for deploying principal stratification and causal mediation analysis in tandem to characterize the extent to which decreased sulphur dioxide emissions from 410 power plants across the USA impact mortality and hospitalization outcomes across Medicare beneficiaries residing across 12370 locations in a manner that is mediated through reductions of ambient fine particulate pollution. The result is the first epidemiological investigation integrating causal inference methodology with direct measurements of coal emissions, pollution transport, ambient pollution and human health in a single analysis, indicating the potential for data science at the intersection of statistics, epidemiology and atmospheric science.