Spatial Modeling for Capturing the Effects of Point Sources

Abstract

The point source is the most common type of source to be modeled for its effect on air pollution. Point sources provide auxiliary information that may impact both the mean and covariance structure of measured responses, but these possible impacts are often overlooked by spatial modelers. In this dissertation, we investigate the impact of point sources on both the mean and covariance by incorporating subject-matter expertise to obtain large- and small-scale models of variability for two real applications. Inference proceeds according to the Bayesian hierarchical paradigm and is implemented using Markov chain Monte Carlo methods.

The first application focuses on electric potential in a field containing a metal pole. Variability due to the point source is captured by our newly proposed autoregressive point source model. This parametric approach allows a formal test of effectiveness of the point source, which is significant for capturing small-scale variability of the electric potential process. The second application focuses on pollution monitoring by the Kincaid experiments. By combining error components with deterministic atmospheric dispersion models (ADMs) to form our ECA-ADM, we formalize point source modeling to obtain prediction uncertainties. These error components are based on the default neighborhood structures created by the point source and already recognized by ADMs. In addition, a new spatial process, called the clustered double conditional autoregressive (CDCAR) model, is proposed to accommodate point sources. CDCAR includes commonly used processes, such as the conditional autoregressive and two-fold conditional autoregressive models, as special cases.