Bayesian analysis of daily maximum ozone levels

Ground level ozone is one of the six criteria primary pollutants that is monitored by the United States Environmental Protection Agency. Statistical methods are increasingly being used to model ground level ozone concentration data. This thesis is motivated by the need to perform practical data analysis, and to develop methods for modelling of ozone concentration data observed over a vast study region in the eastern United States (US. For the purposes of analysis, we use two space-time modelling strategies: the dynamic linear models (DLM) and the auto-regressive (AR) models and obtain predictions and forecasts for set aside validation data. These methods are developed under the Bayesian paradigm and MCMC sampling techniques are used to explore the posterior and predictive distributions. Particularly, for analysis, we use a subset data set from the state of New York to illustrate the methods. Both the DLM and AR modelling approaches are compared in detail using the predictive and forecast distributions induced by them. The comparisons are facilitated by a number of theoretical results. These show better properties for the AR models under some conditions, which have been shown to hold for the real life example that we considered. To address the challenge of modelling large dimensional spatio-temporal ozone concentration data, we adopt Gaussian predictive processes (GPP) technique and propose a rich hierarchical spatio-temporal AR model. The important utility of this method lies in the ability to predict the primary ozone standard at any given location for the modelled period from 1997-2006 in the eastern US. Different sensitivity analyses are performed, and, in addition, hold-out data sets are used for model validation. Specifically, this new modelling approach has been illustrated for evaluating meteorologically adjusted trends in the primary ozone standard in the eastern US over the 10 year period. This helps in understanding spatial patterns and trends in ozone levels, which in turn will help in evaluating emission reduction policies that directly affect many industries. Forecasting of ozone levels is also an important problem in air pollution monitoring. We compare different spatio-temporal models for their forecasting abilities. The GPP based models provide the best forecast for set aside validation data. In addition, in this thesis we use computer simulation model output as an explanatory variable for modelling the observed ozone data. Thus, the proposed methods can also be seen as a spatio-temporal downscaler model for incorporating output from numerical models, where the grid-level output from numerical models is used as a covariate in the point level model for observed data. This type of space and time varying covariate information enriches the regression settings like the methods used in this thesis. Currently there is no package available that can fit space-time environmental data using Bayesian hierarchical spatio-temporal models. In this thesis we, therefore, develop a software package named spTimer in R. The spTimer package with its ability to fit, predict and forecast using a number of Bayesian hierarchical space-time models can be used for modelling a wide variety of large space-time environmental data. This package is built in C language to be computationally efficient. However, this C-code is hidden from the user and the methods can be implemented by anyone familiar with the R language. This thesis can be extended in several ways for example, for multivariate data, for non-Gaussian first stage data, and for data observed in environmental monitoring of stream networks.