No abstract

No abstract

Summary. Air pollution is a major risk factor for global health, with 3 million deaths annually being attributed to fine particulate matter ambient pollution (PM 2:5 ). The primary source of information for estimating population exposures to air pollution has been measurements from ground monitoring networks but, although coverage is increasing, regions remain in which monitoring is limited. The data integration model for air quality supplements ground monitoring data with information from other sources, such as satellite retrievals of aerosol optical depth and chemical transport models. Set within a Bayesian hierarchical modelling framework, the model allows spatially varying relationships between ground measurements and other factors that estimate air quality. The model is used to estimate exposures, together with associated measures of uncertainty, on a high resolution grid covering the entire world from which it is estimated that 92% of the world's population reside in areas exceeding the World Health Organization's air quality guidelines.

Summary We describe a range of routine statistical problems in which marginal posterior distributions derived from improper prior measures are found to have an unBayesian property—one that could not occur if proper prior measures were employed. This paradoxical possibility is shown to have several facets that can be successfully analysed in the framework of a general group structure. The results cast a shadow on the uncritical use of improper prior measures. A separate examination of a particular application of Fraser's structural theory shows that it is intrinsically paradoxical under marginalization.

No abstract