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Hierarchical Bayesian Regression With Application In Spatial Modeling And Outlier Detection, Ghadeer Mahdi
Hierarchical Bayesian Regression With Application In Spatial Modeling And Outlier Detection, Ghadeer Mahdi
Graduate Theses and Dissertations
This dissertation makes two important contributions to the development of Bayesian hierarchical models. The first contribution is focused on spatial modeling. Spatial data observed on a group of areal units is common in scientific applications. The usual hierarchical approach for modeling this kind of dataset is to introduce a spatial random effect with an autoregressive prior. However, the usual Markov chain Monte Carlo scheme for this hierarchical framework requires the spatial effects to be sampled from their full conditional posteriors one-by-one resulting in poor mixing. More importantly, it makes the model computationally inefficient for datasets with large number of units. …