Date of Graduation
Master of Science in Statistics and Analytics (MS)
Second Committee Member
Pure sciences, Bayesian, Spatial, Variable selection
This thesis first describes the general idea behind Bayes Inference, various sampling methods based on Bayes theorem and many examples. Then a Bayes approach to model selection, called Stochastic Search Variable Selection (SSVS) is discussed. It was originally proposed by George and McCulloch (1993). In a normal regression model where the number of covariates is large, only a small subset tend to be significant most of the times. This Bayes procedure specifies a mixture prior for each of the unknown regression coefficient, the mixture prior was originally proposed by Geweke (1996). This mixture prior will be updated as data becomes available to generate a posterior distribution that assigns higher posterior probabilities to coefficients that are significant in explaining the response. Spatial modeling method is described in this thesis. Prior distribution for all unknown parameters and latent variables are specified. Simulated studies under different models have been implemented to test the efficiency of SSVS. A real dataset taken by choosing a small region from the Cape Floristic Region in South Africa is used to analyze the plants distribution in that region. The original multi-cateogory response is transformed into a presence and absence (binary) response for simpler analysis. First, SSVS is used on this dataset to select the subset of significant covariates. Then a spatial model is fitted using the chosen covariates and, post-estimation, predictive map of posterior probabilities of presence and absence are obtained for the study region. Posterior estimates for the true regression coefficients are also provided along with map for spatial random effects.
Tang, Xiahan, "A Bayesian Variable Selection Method with Applications to Spatial Data" (2017). Theses and Dissertations. 1956.