Type of Document Dissertation Author Velasco-Cruz, Ciro Author's Email Address firstname.lastname@example.org URN etd-05182012-130009 Title Spatially Correlated Model Selection (SCOMS) Degree PhD Department Statistics Advisory Committee
Advisor Name Title Leman, Scotland C. Committee Co-Chair Smith, Eric P. Committee Co-Chair Guo, Feng Committee Member House, Leanna L. Committee Member Keywords
- Spatial statistics
- Ising prior
- Non-stationary spatial fields
- Variable Selection
Date of Defense 2012-05-04 Availability unrestricted AbstractIn this dissertation, a variable selection method for spatial data is developed. It is assumed that the spatial process is non-stationary as a whole but is piece-wise stationary. The pieces where the spatial process is stationary are called regions. The variable selection approach accounts for two sources of correlation: (1) the spatial correlation of the data within the regions, and (2) the correlation of adjacent regions.
The variable selection is carried out by including indicator variables that characterize the significance of the regression coefficients. The Ising distribution as prior for the vector of indicator variables, models the dependence of adjacent regions.
We present a case study on brook trout data where the response of interest is the presence/absence of the fish at sites in the eastern United States. We find that the method outperforms the case of the probit regression where the spatial field is assumed stationary and isotropic. Additionally, the method outperformed the case where multiple regions are assumed independent of their neighbors.
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