  A typical problem in air pollution epidemiology is exposure assessment for
individuals for which health data are available. Due to the sparsity of
monitoring sites and the limited temporal frequency with which measurements of
air pollutants concentrations are collected (for most pollutants, once every 3
or 6 days), epidemiologists have been moving away from characterizing ambient
air pollution exposure solely using measurements. In the last few years,
substantial research efforts have been placed in developing statistical methods
or machine learning techniques to generate estimates of air pollution at finer
spatial and temporal scales (daily, usually) with complete coverage. Some of
these methods include: geostatistical techniques, such as kriging; spatial
statistical models that use the information contained in air quality model
outputs (statistical downscaling models); linear regression modeling approaches
that leverage the information in GIS covariates (land use regression); or
machine learning methods that mine the information contained in relevant
variables (neural network and deep learning approaches). Although some of these
exposure modeling approaches have been used in several air pollution
epidemiological studies, it is not clear how much the predicted exposures
generated by these methods differ, and which method generates more reliable
estimates. In this paper, we aim to address this gap by evaluating a variety of
exposure modeling approaches, comparing their predictive performance and
computational difficulty. Using PM$_{2.5}$ in year 2011 over the continental
U.S. as case study, we examine the methods' performances across seasons, rural
vs urban settings, and levels of PM$_{2.5}$ concentrations (low, medium, high).
