In this dissertation, we develop a model selection and estimation methodology for nonstationary spatial fields. Large, spatially correlated data often cover a vast geographical area. However, local spatial regions may have different mean and covariance structures. Our methodology accomplishes three goals: (1) cluster locations into small regions with distinct, stationary models, (2) perform Bayesian model selection within each cluster, and (3) correlate the model selection and estimation in nearby clusters. We utilize the Conditional Autoregressive (CAR) model and Ising distribution to provide intra-cluster correlation on the linear effects and model inclusion indicators, while modeling inter-cluster correlation with separate Gaussian processes. We apply our model selection methodology to a dataset involving the prediction of Brook trout presence in subwatersheds across Pennsylvania. We find that our methodology outperforms the stationary spatial model and that different regions in Pennsylvania are governed by separate Gaussian process regression models. / Ph. D. / In this dissertation, we develop a statistical methodology for analyzing data where observations are related to each other due to spatial proximity. Our overall goal is to determine which attributes are important when predicting the response of interest. However, the effect and importance of an attribute may differ depending on the spatial location of the observation. Our methodology accomplishes three goals: (1) partition the observations into small spatial regions, (2) determine which attributes are important within each region, and (3) enforce that the importance of variables should be similar in regions that are near each other. We apply our technique to a dataset involving the prediction of Brook trout presence in subwatersheds across Pennsylvania.
| Identifer | oai:union.ndltd.org:VTETD/oai:vtechworks.lib.vt.edu:10919/84161 |
| Date | 18 July 2018 |
| Creators | Fry, James Thomas |
| Contributors | Statistics, Leman, Scotland C., Resler, Lynn M., Gramacy, Robert B., Smith, Eric P. |
| Publisher | Virginia Tech |
| Source Sets | Virginia Tech Theses and Dissertation |
| Detected Language | English |
| Type | Dissertation |
| Format | ETD, application/pdf |
| Rights | In Copyright, http://rightsstatements.org/vocab/InC/1.0/ |
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