Document Type


Date of Degree

Summer 2016

Degree Name

PhD (Doctor of Philosophy)

Degree In


First Advisor

Cowles, Mary K.

First Committee Member

Bognar, Matthew

Second Committee Member

Smith, Brian

Third Committee Member

Tierney, Luke-jon

Fourth Committee Member

Zimmerman, Dale


A popular model for spatial association is the conditional autoregressive (CAR) model, and generalizations exist in the literature that utilize intrinsic CAR (ICAR) models within spatial hierarchical models. One generalization is the class of Bayesian hierarchical normal ICAR models, abbreviated HNICAR. The Bayesian HNICAR model can be used to smooth areal or lattice data, estimate the directional strength of spatio-temporal associations, and make posterior predictions at each point in space or time. Furthermore, the Bayesian HNICAR model allows for sample-based posterior inference about model parameters and predictions. R package CARrampsOcl enables fast, independent sampling-based inference for a Bayesian HNICAR model when data are complete and the spatial precision matrix is expressible as a Kronecker sum of lower order matrices. This thesis presents an independent sampling algorithm to accommodate incomplete data and arbitrary precision structures, a parallelized implementation of the algorithm that can be executed on a wide range of hardware, including NVIDIA and AMD graphical processing units (GPUs) and multicore Intel CPUs, analysis of the effects of missingness on the posterior distribution of model parameters and predictive densities, and a survey of model comparison methods for CAR models. The merits of the model and algorithm are demonstrated through both simulation and analysis of an environmental data set.


Bayesian, Computing, Heterogeneous, Hierarchical, OpenCL, Parallel


xii, 105 pages


Includes bibliographical references (pages 96-105).


Copyright 2016 Harsimran S. Somal