  Air pollution is a major risk factor for global health, with both ambient and
household air pollution contributing substantial components of the overall
global disease burden. One of the key drivers of adverse health effects is fine
particulate matter ambient pollution (PM$_{2.5}$) to which an estimated 3
million deaths can be attributed annually. The primary source of information
for estimating exposures has been measurements from ground monitoring networks
but, although coverage is increasing, there remain regions in which monitoring
is limited. Ground monitoring data therefore needs to be supplemented with
information from other sources, such as satellite retrievals of aerosol optical
depth and chemical transport models. A hierarchical modelling approach for
integrating data from multiple sources is proposed allowing spatially-varying
relationships between ground measurements and other factors that estimate air
quality. Set within a Bayesian framework, the resulting Data Integration Model
for Air Quality (DIMAQ) is used to estimate exposures, together with associated
measures of uncertainty, on a high resolution grid covering the entire world.
Bayesian analysis on this scale can be computationally challenging and here
approximate Bayesian inference is performed using Integrated Nested Laplace
Approximations. Model selection and assessment is performed by cross-validation
with the final model offering substantial increases in predictive accuracy,
particularly in regions where there is sparse ground monitoring, when compared
to current approaches: root mean square error (RMSE) reduced from 17.1 to 10.7,
and population weighted RMSE from 23.1 to 12.1 $\mu$gm$^{-3}$. Based on
summaries of the posterior distributions for each grid cell, it is estimated
that 92% of the world's population reside in areas exceeding the World Health
Organization's Air Quality Guidelines.
