Bayesian Inference Based on Nonparametric Regression for Highly Correlated and High Dimensional Data

Establishing relationships among observed variables is important in many research studies. However, the task becomes increasingly difficult in the presence of unidentified complexities stemming from interdependencies among multi-dimensional variables and variability across subjects. This dissertation presents three novel methodological approaches to address these complex associations between highly correlated and high dimensional data. Firstly, group multi-kernel machine regression (GMM) is proposed to identify the association between two sets of multidimensional functions, offering flexibility to effectively capture the complex association among high-dimensional variables. Secondly, semiparametric kernel machine regression under a Bayesian hierarchical structure is introduced for matched case-crossover studies, enabling flexible modeling of multiple covariate effects within strata and their complex interactions, denoted as fused kernel machine regression (Fused-KMR). Lastly, it presents a Bayesian hierarchical framework designed to identify multiple change points in the relationship between ambient temperature and mortality rate. This framework, unlike traditional methods, treats change points as random variables, enabling the modeling of nonparametric functions that vary by region and is denoted as a multiple random change point (MRCP). Simulation studies and real-world applications illustrate the effectiveness and advantages of these approaches in capturing intricate associations and enhancing predictive accuracy.

Name thesis:degree_name

Doctor of Philosophy

Level thesis:degree_level

doctoral

Discipline thesis:degree_discipline

Statistics

Department dc:contributor.department

Statistics

Grantor dc:publisher

Virginia Tech

Year dc:date.issued

2024

Author dc:creator

• Yun, Young Ho

Chair dc:contributor.committeechair

• Kim, Inyoung

Committee members dc:contributor.committeemember

• Franck, Christopher Thomas
• Van Mullekom, Jennifer Huffman
• Deng, Xinwei

• Kernel Machine Regression

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Language dc:language.iso

en

Dc Identifier Other

vt_gsexam:42305

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/123800