Date of Award
Fall 2025
Document Type
Open Access Dissertation
Department
Statistics
First Advisor
Stella Coker Watson Self
Abstract
Group testing is a procedure that tests pooled, instead of individual, biospecimens. If a pool tests positive, subsequent tests are usually conducted on the individuals who contributed to the pool to determine their disease status; if a pool tests negative, all samples in the pool are considered disease-free. Under relatively low disease prevalence, group testing reduces the required number of diagnostic tests and the associated costs. The first two projects in this dissertation develop innovative statistical methodologies for group testing data. The first project introduces two Bayesian spatio-temporal regression models for discrete-time areal group testing data. These models incorporate spatio-temporal dependency and allow for the estimation of fixed, spatio-temporal random effects, and the sensitivity and specificity of diagnostic tests. Our model can also produce forecast maps for infectious diseases. The second project addresses computational bottlenecks associated with existing group testing models by implementing the variational Bayes (VB) algorithm. Our method demonstrates accurate estimation and reliable inference compared to existing Markov chain Monte Carlo (MCMC) algorithms for Bayesian models and expectation-maximization algorithm for group testing data but offers substantially improved computational efficiency, particularly in the large-scale data setting.
Areal or lattice data is a basic type of spatial data capturing aggregated outcomes associated with a finite number of areal units. Ordinal areal data is a form of categorical areal data in which associated outcomes or categories for areal units follow a nature order, such as social vulnerability levels (low, low-medium, medium-high and high) for United States counties. The third project introduces the ordinal areal proportion function (OAPF) and develops a multi-stage testing procedure to detect any clustering pattern from ordinal areal data. In summary, this dissertation advances the statistical modeling and computational techniques for group testing and ordinal areal data, with direct applications in public health, disease surveillance, and epidemiological research.
Rights
© 2025, Xingpei Zhao
Recommended Citation
Zhao, X.(2025). Advanced Bayesian Models for Group Testing Data and Cluster Detection in Ordinal Areal Data. (Doctoral dissertation). Retrieved from https://scholarcommons.sc.edu/etd/8662