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Nonpenalized Model Selection via Generalized Fiducial Inference and Bayesian Hidden Markov Models
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| 자료유형 | 학위논문 |
|---|---|
| 서명/저자사항 | Nonpenalized Model Selection via Generalized Fiducial Inference and Bayesian Hidden Markov Models. |
| 개인저자 | Williams, Jonathan P. |
| 단체저자명 | The University of North Carolina at Chapel Hill. Statistics and Operations Research. |
| 발행사항 | [S.l.]: The University of North Carolina at Chapel Hill., 2019. |
| 발행사항 | Ann Arbor: ProQuest Dissertations & Theses, 2019. |
| 형태사항 | 172 p. |
| 기본자료 저록 | Dissertations Abstracts International 81-04A. Dissertation Abstract International |
| ISBN | 9781085798785 |
| 학위논문주기 | Thesis (Ph.D.)--The University of North Carolina at Chapel Hill, 2019. |
| 일반주기 |
Source: Dissertations Abstracts International, Volume: 81-04, Section: A.
Advisor: Hannig, Jan. |
| 이용제한사항 | This item must not be sold to any third party vendors. |
| 요약 | This dissertation is comprised predominantly of two topics of research. On the first topic, standard penalized methods of variable selection and parameter estimation in the linear regression model rely on the magnitude of coefficient estimates to decide which variables to include in the final model. However, coefficient estimates are unreliable when the design matrix is collinear. To overcome this challenge an entirely new perspective on model selection is presented within a generalized fiducial inference framework. This new procedure is able to effectively account for linear dependencies among subsets of covariates in a high-dimensional setting where p can grow almost exponentially in n. Furthermore, with a typical sparsity assumption, it is shown that the proposed method is consistent in the sense that the probability of the true sparse subset of covariates converges in probability to 1 as n approaches infinity, or as n and p approach infinity.The model selection methodology is also extended from the linear regression setting to the vector autoregressive (VAR) setting. In the extension, we construct methodology via the epsilon-admissible subsets (EAS) approach for posterior-like inference of relative model probabilities over all sets of active/inactive components of the VAR transition matrix. We provide a mathematical proof of pairwise and strong graphical selection consistency for the EAS approach for stable VAR(1) models, and demonstrate numerically that it is an effective strategy in high-dimensional settings.The second topic is motivated by the Mayo Clinic Study of Aging data for 4742 subjects since 2004, and how it can be used to draw inference on the role of aging in the development of dementia. We construct a hidden Markov model (HMM) to represent progression of dementia from states associated with the buildup of amyloid plaque in the brain, and the loss of cortical thickness. A hierarchical Bayesian approach is taken to estimate the parameters of the HMM with a truly time-inhomogeneous infinitesimal generator matrix, and response functions of the continuous-valued biomarker measurements are cut-point agnostic. |
| 일반주제명 | Statistics. Operations research. Economics. Aging. |
| 언어 | 영어 |
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: 이 자료의 원문은 한국교육학술정보원에서 제공합니다. |
