Bayesian Inference Based on Nonparametric Regression for Highly Correlated and High Dimensional Data
| dc.contributor.author | Yun, Young Ho | en |
| dc.contributor.committeechair | Kim, Inyoung | en |
| dc.contributor.committeemember | Franck, Christopher Thomas | en |
| dc.contributor.committeemember | Van Mullekom, Jennifer Huffman | en |
| dc.contributor.committeemember | Deng, Xinwei | en |
| dc.contributor.department | Statistics | en |
| dc.date.accessioned | 2024-12-14T09:00:10Z | en |
| dc.date.available | 2024-12-14T09:00:10Z | en |
| dc.date.issued | 2024-12-13 | en |
| dc.description.abstract | 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. | en |
| dc.description.abstractgeneral | Establishing relationships among observed variables is important in many research studies. However, the task becomes increasingly difficult due to unidentified complexities stemming from interdependencies among multi-dimensional inputs. This dissertation presents three novel methodological approaches to address these complex associations, given the large amount of data in which the number of samples is much smaller than the number of variables. Firstly, a flexible regression model is proposed to identify the association between two sets of multidimensional functions to effectively capture the complex association given large quantities of data. Secondly, an efficient regression model is introduced for a dataset with cases and controls matched over time, enabling flexible modeling of multiple variable effects for each subject and their complex interactions. Lastly, it presents a framework to identify multiple change points in the relationship between ambient temperature and mortality rate. This framework allows change points to vary by region, enabling the modeling of complex functions. Simulation studies and real-world applications illustrate the effectiveness and advantages of these approaches in capturing intricate associations and enhancing predictive accuracy. | en |
| dc.description.degree | Doctor of Philosophy | en |
| dc.format.medium | ETD | en |
| dc.identifier.other | vt_gsexam:42305 | en |
| dc.identifier.uri | https://hdl.handle.net/10919/123800 | en |
| dc.language.iso | en | en |
| dc.publisher | Virginia Tech | en |
| dc.rights | In Copyright | en |
| dc.rights.uri | http://rightsstatements.org/vocab/InC/1.0/ | en |
| dc.subject | Kernel Machine Regression | en |
| dc.title | Bayesian Inference Based on Nonparametric Regression for Highly Correlated and High Dimensional Data | en |
| dc.type | Dissertation | en |
| thesis.degree.discipline | Statistics | en |
| thesis.degree.grantor | Virginia Polytechnic Institute and State University | en |
| thesis.degree.level | doctoral | en |
| thesis.degree.name | Doctor of Philosophy | en |