Data augmentation for the handling of censored spatial data

Fridley, Brooke
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This dissertation provides a solution to the analysis of spatial censored data. Spatially dependent data occurs in a variety of applications in which observations are associated with a spatial location. In environmental data, it is not uncommon for measurements of contamination to fall below a level of detection (LOD). There are many statistical methods for the analysis of censored data when the observations are independent, but what does one do when spatial correlation is present? A solution presented in this dissertation is to use the idea of data augmentation for the analysis censored spatial data.;The first paper will look at a Bayesian geostatistical model. In addition to parameter estimation and inference, a main focus of many analyzes is spatial prediction. A prediction method will also be presented and illustrated involving censored data from two studies, one involving dioxin contamination in Missouri and one looking at site polluted with heavy metals. Comparison between the data augmentation method and the methods of replacing the censored values with LOD and LOD/2 are also be illustrated.;The second paper explores the use of data augmentation for censored spatial data in the context of a Bayesian conditionally specified Gaussian model. As opposed to the Bayesian geostatistical model, the focus of this paper is not on prediction, but on parameter estimation and subsequent inference. The Missouri dioxin study and the metal contamination site will be used to illustrate the method, along with comparison to the common method of replacing the censored observations with the LOD/2 or LOD.;In the third paper, results from an extensive simulation study conducted to investigate the effect of different factors on the effectiveness of the data augmentation procedure for the handling of censored spatial data, are presented and discussed. In addition to simulation studies investigating factors that may impact the data augmentation procedure, two additional simulation studies were conducted to look at the general adequacy of the augmentation procedure for both the geostatistical and conditionally specified Bayesian models.