Evaluation and Application of the Gaussian-Log Gaussian Spatial Model for Robust Bayesian Prediction of Tehran Air Pollution Data

Air pollution is one of the major problems of Tehran metropolis. Regarding the fact that Tehran is surrounded by Alborz Mountains from three sides, the pollution due to the cars traffic and other polluting means causes the pollutants to be trapped in the city and have no exit without appropriate wind guff. Carbon monoxide (CO) is one of the most important sources of pollution in Tehran air. The concentration of carbon monoxide increases remarkably at the city regions with heavy traffic. Due to the negative effects of this gas on breathing metabolism and people brain activities, the modeling and classifying of the CO amounts in order to control and reduce it, is very noteworthy. For this reason Rivaz et al. (2007) using a Gaussian model presented the space-time analysis of the Tehran air pollution based on the observations from 11 stations for measuring the air pollution. Although assuming the Gaussian observations causes the simplicity of the inferences such as prediction, but often this assumption is not true in reality. One of the outrage factors from normality assumption is the outlying observations. For example in Tehran air pollution issue, the Sorkhe Hesar station indicates very low pollution compare to the other stations due to locating in a forest region. Therefore this observation could be considered as an outlying observation. Whereas the presence of such data causes the thickening of distribution tails and increasing the kurtosis coefficient, therefore in this situation normal distribution which has a narrower tails can not be used. Generally identifying and modeling the outlying observations is one of the main issues that statistician have been faced with since long time ago and many different solutions have been presented so far to overcome the problems arising from such observations. Amongst all these solutions, robust methods can be mentioned (Militino et al., 2006, and Cerioli and Riani, 1999). In these methods with normality observations assumption, the aim is to present a robust analysis. But there might be an outlying observation which belongs to the same pattern of other data. In this case applying those distributions with thicker tails compare to the normal distribution could be useful. This matter was evaluated by Jeffreys (1961) for the first time. Maronna (1976) and Lang et al. (1989) evaluated the verifying maximum likelihood estimation for the model in which the errors imitating the student-t distribution. West (1984) also used the scale mixture of normal distribution families for modeling the outlying observations. Fernandez and Steel (2000) also evaluated the existence of posterior distribution and its moments by introducing the improper prior distributions for West model. In the field of geostatistical data, Palacios and Steel (2006) introduced the extended Gaussian model as below by considering the errors distribution from the scale mixture of normal distributions family....(to countinue here)