Literature Review
Air pollution has been over the years considered to have detrimental effect on the health of living things including human beings with a perfect example being the London smog episode that occurred in 1952 (Pannullo, Lee, Waclawski, and Leyland, 2016). Jerrett et al. (2005) state exposure to pollution can be modelled differently from using simple proximity measures (Buzzelli and Jerrett, 2003), land use regression models (Ryan and LeMasters, 2007) to complex atmospheric dispersion (Caputo et al., 2003), hybrid models (Cauvin et al., 2001) and integrated meteorological‐emission models (Gaines Wilson and Zawar‐Reza, 2006). De Hoogh et al. (2014) suggests that to get unambiguous and accurate exposure patterns, multiple model strategies should be utilised. While the present study will utilise functional data analysis, it is significant to review how previous studies have used other statistical methods to estimate pollution exposure. Among the most common used air modelling methods are Bayesian methods and there lacks extensive literature non-Bayesian methods often referred to as ‘classical statistics’ or ‘hypothesis testing.’
Pannullo et al. (2016) conducted a study using the Bayesian model averaging approach in combining outcomes from various statistical models when investigating the sensitivity of the relationship between pollution and health in West Central Scotland concluding there is positive correlation. Similarly, Liu, Guo, Mao, and Yang, (2008) developed a Bayesian hierarchical model with an aim of predicting urban air quality using multivariate statistical methods such as discriminant analysis, correlation analysis and hierarchical cluster analysis. In another study, Pirani, Gulliver, Fuller, and Blangiardo, (2014) utilised a Bayesian hierarchical approach in predicting short-term exposure to pollution of article in London. The results of these studies were similar in particular because of the use of short-term modelling. In their study, Molitor et al. (2016) used a new statistical procedure which adapts measurement error models in estimation of missing exposure data in assessment of health effects. Specifically, the method used a Bayesian framework and concluded that the method was critical in improving estimates compared to other approaches (Molitor et al. 2016). However, in their study of how air pollution impacts China, Wang, Dai, and Wang, (2017) found that there was difference BP neural networks with Bayesian regularization and non-Bayesian BP neural networks.
According to Lee, Rushworth, and Sahu, (2014) estimating the long-term impact of air pollution could prove a challenge specifically when modelling spatial small area. In doing their research, lee et al. (2014) opted to use a Bayesian localized conditional autoregressive model which is considered flexible spatially and enabled the results to show critical health effects of nitrogen dioxide and particulate matter air pollution. Consequently, Vitolo, Scutari, Ghalaieny, Tucker, and Russell, (2018) used a Bayesian Networks with a multivariate approach to investigate health outcomes, exposure levels, and environmental factors in the United Kingdom. The results of the study depicted that for weather and pollution variables, in a sample, the model tests well but at the same time has good predictive power when not in a sample. Afshar, and Delavar, (2007) argue that among the major problems that mega cities face air pollution and increasing traffic due to rising population growth as well as constant development of these cities. Afshar, and Delavar, (2007) developed a GIS-based model to predict air pollution in the year 2004 using the data available of 2003 and 2002. The results concluded efficiency of the canyon model when complete data was utilised. Another study was carried out by Dominici, Zeger, and Samet, (2000) using a multi-stage Poisson regression model to evaluate the impact of exposure measurement errors while recently, Kobus, and Kostrzewa, (2015) used spatial data processing tools to conduct quality assessments of air.
While there is less literature on using non- Bayesian models in modelling air pollution, Gelman, (2008) argues that some of the major problems that limits Bayesian models include adequate time required in thinking through application of the model. Other disadvantages include it is impossible to make evaluation of the statistical method properties and finally they encourage believe in results supporting their preconceptions and oppose those that seems to surprise them.

References
Afshar, H. and Delavar, M.R., 2007. A GIS-based air pollution modeling in Tehran. Environmental Informatics Archives, 5, pp.557-566.
Buzzelli, M., and Jerrett, M. (2003). Comparing proximity measures of exposure to geostatistical estimates in environmental justice research. Global Environmental Change Part B: Environmental Hazards, 5(1), 13–21.
Caputo, M., Giménez, M., and Schlamp, M. (2003). Intercomparison of atmospheric dispersion models. Atmospheric Environment, 37(18), 2435–2449.
Cauvin, S., Moullec, Y. L., Bremont, F., Momas, I., Balducci, F., Ciognard, F.,…Zmirou, D. (2001). Relationships between nitrogen dioxide personal exposure and ambient air monitoring measurements among children in three French metropolitan areas: VESTA study. Archives of Environmental Health: An International Journal, 56(4), 336–341.
Dominici, F., Zeger, S.L. and Samet, J.M., 2000. A measurement error model for time-series studies of air pollution and mortality. Biostatistics, 1(2), pp.157-175.
Gaines Wilson, J., and Zawar‐Reza, P. (2006). Intraurban‐scale dispersion modelling of particulate matter concentrations: Applications for exposure estimates in cohort studies. Atmospheric Environment, 40(6), 1053–1063.
Gelman, A., 2008. Objections to Bayesian statistics. Bayesian Analysis, 3(3), pp.445-449.
Jerrett, M., Arain, A., Kanaroglou, P., Beckerman, B., Potoglou, D., Sahsuvaroglu, T.,…Giovis, C. (2005). A review and evaluation of intraurban air pollution exposure models. Journal of Exposure Analysis and Environmental Epidemiology, 15(2), 185–204.
Kobus, D. and Kostrzewa, J., 2015. The use of spatial data processing tools for air quality assessments-practical examples. Information Systems in Management, 4.
Lee, D., Rushworth, A. and Sahu, S.K., 2014. A Bayesian localized conditional autoregressive model for estimating the health effects of air pollution. Biometrics, 70(2), pp.419-429.
Liu, Y., Guo, H., Mao, G. and Yang, P., 2008. A bayesian hierarchical model for urban air quality prediction under uncertainty. Atmospheric Environment, 42(36), pp.8464-8469.
Molitor, J., Molitor, N.T., Jerrett, M., McConnell, R., Gauderman, J., Berhane, K. and Thomas, D., 2006. Bayesian modeling of air pollution health effects with missing exposure data. American journal of epidemiology, 164(1), pp.69-76.
Pannullo, F., Lee, D., Waclawski, E. and Leyland, A.H., 2016. How robust are the estimated effects of air pollution on health? Accounting for model uncertainty using Bayesian model averaging. Spatial and spatio-temporal epidemiology, 18, pp.53-62.
Pirani, M., Gulliver, J., Fuller, G.W. and Blangiardo, M., 2014. Bayesian spatiotemporal modelling for the assessment of short-term exposure to particle pollution in urban areas. Journal of Exposure Science and Environmental Epidemiology, 24(3), p.319.
Ryan, P. H., and LeMasters, G. K. (2007). A review of land‐use regression models for characterizing intraurban air pollution exposure. Inhalation toxicology, 19(sup1), 127–133.
Vitolo, C., Scutari, M., Ghalaieny, M., Tucker, A. and Russell, A., 2018. Modeling Air Pollution, Climate, and Health Data Using Bayesian Networks: A Case Study of the English Regions. Earth and Space Science, 5(4), pp.76-88.
Vitolo, C., Scutari, M., Ghalaieny, M., Tucker, A. and Russell, A., 2018. Modeling Air Pollution, Climate, and Health Data Using Bayesian Networks: A Case Study of the English Regions. Earth and Space Science, 5(4), pp.76-88.
Wang, Q., Dai, H.N. and Wang, H., 2017. A smart MCDM framework to evaluate the impact of air pollution on city sustainability: a case study from China. Sustainability, 9(6), p.911.