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Activity Number: 368
Type: Contributed
Date/Time: Tuesday, August 2, 2016 : 10:30 AM to 12:20 PM
Sponsor: Section on Bayesian Statistical Science
Abstract #320829 View Presentation
Title: Alternative Approach to Modeling Areal-Level Spatial Data Using Basis Functions
Author(s): Ghadeer Mahdi* and Avishek Chakraborty and Mark Arnold
Companies: University of Arkansas and University of Arkansas and University of Arkansas
Keywords: Areal spatial data ; Basis function ; CAR prior ; Graph Laplacian ; Markov random field

Datasets with observations coming from adjacent areal units or from a lattice are common in scientific applications such as epidemiology and oil exploration studies. For this type of data, the spatial association between observations are modeled using adjacency instead of geographical distance. The typical approach is to use a Markov random field prior for spatial effects using the full conditional distributions. When number of units in the lattice is very large, the MCMC scheme suffers from high auto-correlation and huge runtime. We propose an alternative approach to this where we build a spatial regression model using the spectral properties of the adjacency matrix. We use a truncated basis function expansion to approximate the spatial effect. To enhance flexibility and applicability of our approach, we treat the level of truncation as a parameter as well. This allows the data to choose as many basis functions as it needs, encouraging sparsity whenever possible. We show that the commonly used conditional autoregressive prior is a special case of the proposed model. We present examples from simulation studies as well as real data analysis to show the performance of our method.

Authors who are presenting talks have a * after their name.

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