Extreme air pollutant data analysis using classical and Bayesian approaches

Extreme value (EV) theory has raised researcher intention for modeling and forecasting of catastrophic or higher risk events. The concept of EV theory affords attention to the tails of distribution where standard models are proved unreliable. Generalized extreme value (GEV) distribution and generalized Pareto (GP) distribution are two main models in EV theory based on block maxima and threshold exceedances approaches. These two models are obviously different in terms of the sampling routine used in the formation of the extreme series. However, decisions on block sizes and threshold selection should be made by taking into consideration the limiting distribution properties. Inferences on the extremes of environmental events are essential as guidelines in designing structures in order to survive under the utmost extreme conditions. Extreme air pollutants caused various effects associated to human health and material damages. In many cases, the pollutants are responsible for huge impacts on economic performances. The EV theory is applied to model the extreme PM10 pollutant for three air monitoring stations in Johor. This study started with the analysis of extreme PM10 data based on maximum likelihood estimation technique. Several block sizes were chosen to compare the model fit and hence estimate the return level. Using threshold exceedances technique,the selection of threshold value was made using mean residual life plot and threshold choice plot. Comparable estimates are found when the numbers of samples for both techniques are almost similar. Alternatively, Bayesian framework is implemented to allow priors or additional information concerning the data into the analysis which expectantly improve the model fit. Bayesian inference in the context of EV theory obviously overcomes the scarcity of through the development of simulation based techniques such as Markov chain Monte Carlo (MCMC). Two MCMC techniques are considered for the inferences namely Metropolis-Hastings (MH) algorithm and the Multiple-try Metropolis (MTM) algorithm. MTM algorithm is an extension of MH algorithm, designed to improve the convergence of MH algorithm by performing parallel computation. In general, both methods are performing well for analyzing extreme model but numerical results show that MTM method performs slightly better than MH method in terms of efficiency and convergency to the stationary distribution. The univariate and bivariate extreme processes have been considered extensively using a frequentist perspective and recently there has been an increasing interest in the application of Bayesian methods to EV problems. Generally the univariate extreme inference has been considered commonly in Bayesian perspective. Bayesian techniques for bivariate model have not yet received much attention due to the hitches in dealing with much more parameters. Literature on Bayesian extremes based on MCMC techniques are dealing with either Gibbs sampling method or MH method, or the combination of both methods. This research implemented the MTM method as an alternative for modeling of univariate and bivariate extremes with non-informative priors. Bayesian technique for bivariate monthly maxima data from each pair of sites were employed to analyze the dependencies between two stations.

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