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Bayesian Hidden Markov Model in Multiple Testing on Dependent Count Data

Su, Weizhe
http://rave.ohiolink.edu/etdc/view?acc_num=ucin1613751403094066

Abstract Details

2020, PhD, University of Cincinnati, Arts and Sciences: Mathematical Sciences.
Multiple testing on large-scale dependent count data faces challenges in two basic modeling elements, that is, modeling of the dependence structure across observations and the distribution specification on the null and non-null states. We propose three Poisson hidden Markov models (PHMM) under the Bayesian hierarchical model framework to handle these challenges. The dependence structure across hypotheses is modeled through the hidden Markov process. To address the challenge of the distribution specification under the non-null state, several model selection methods are employed and compared to determine the number of mixture components in the non-null distribution. Furthermore, we examine two different ways to include covariate effects, PHMM with homogeneous covariate effects (PHMM-HO) and PHMM with heterogeneous covariate effects (PHMM-HE). Modeling covariate effects helps take consideration of multiple factors which are directly or indirectly related to the hypotheses under investigation. We carry out extensive simulation studies to demonstrate the performance of the proposed hidden Markov models. The stable and robust results show the significant advantages of our proposed models in handling complex data structure in dependent counts. Multiple hypotheses testing with PHMM is valid and optimal compared with a group of commonly used testing procedures. Both PHMM-HO and PHMM-HE improve the multiple testing performance and are able to detect the dynamic data pattern along with the covariate effects.
Xia Wang, Ph.D. (Committee Chair)
Hang Joon Kim, Ph.D. (Committee Member)
Siva Sivaganesan, Ph.D. (Committee Member)
Seongho Song, Ph.D. (Committee Member)
Bin Zhang, Ph.D. (Committee Member)
110 p.
Statistics
Bayesian hierarchical model; Hidden Markov model; Multiple hypotheses testing; Poisson regression; Sampling based marginal likelihood

Recommended Citations

Citations

  • Su, W. (2020). Bayesian Hidden Markov Model in Multiple Testing on Dependent Count Data [Doctoral dissertation, University of Cincinnati]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1613751403094066

    APA Style (7th edition)

  • Su, Weizhe. Bayesian Hidden Markov Model in Multiple Testing on Dependent Count Data. 2020. University of Cincinnati, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=ucin1613751403094066.

    MLA Style (8th edition)

  • Su, Weizhe. "Bayesian Hidden Markov Model in Multiple Testing on Dependent Count Data." Doctoral dissertation, University of Cincinnati, 2020. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1613751403094066

    Chicago Manual of Style (17th edition)

ucin1613751403094066
38
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This open access ETD is published by University of Cincinnati and OhioLINK.