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Bayesian Hierarchical Modeling for Dependent Data with Applications in Disease Mapping and Functional Data Analysis

Zhang, Jieyan
http://rave.ohiolink.edu/etdc/view?acc_num=ucin1649768302824249

Abstract Details

2022, PhD, University of Cincinnati, Arts and Sciences: Mathematical Sciences.
Bayesian hierarchical modeling has a long history but did not receive wide attention until the past few decades. Its advantages include flexible structure and capability of incorporating uncertainty in the inference. This dissertation develops two Bayesian hierarchical models for the following two scenarios: first, spatial data of time to disease outbreak and disease duration, second, large or high dimensional functional data that may cause computational burden and require rank reduction. In the first case, we use cucurbit downy mildew data, an economically important plant disease data recorded in sentinel plot systems from 23 states in the eastern United States in 2009. The joint model is established on the dependency of the spatially correlated random effects, or frailty terms. We apply a parametric Weibull distribution to the censored time to disease outbreak data, and a zero-truncated Poisson distribution to the disease duration data. We consider several competing process models for the frailty terms in the simulation study. Given that the generalized multivariate conditionally autoregressive (GMCAR) model, which contains correlation and spatial structure, provides a preferred DIC and LOOIC results, we choose the GMCAR model for the real data. The proposed joint Bayesian hierarchical model indicates that states in the mid-Atlantic region tend to have a high risk of disease outbreak, and in the infected cases, they tend to have a long duration of cucurbit downy mildew. The second Bayesian hierarchical model smooths functional curves simultaneously and nonparametrically with improved computational efficiency. Similar to the frequentist counterpart, principal analysis by conditional expectation, the second model reduces rank through the multi-resolution spline basis functions in the process model. The proposed method outperforms the commonly used B-splines basis functions by providing a slightly better estimation within a much shorter computing time. The performance of this model is also examined using two real data sets, a sleeping energy expenditure data from an obesity study conducted in Baylor College of Medicine, and a human mortality data.
Emily Kang, Ph.D. (Committee Member)
Seongho Song, Ph.D. (Committee Member)
Bledar Konomi, Ph.D. (Committee Member)
Won Chang, Ph.D. (Committee Member)
108 p.
Statistics
Basis function; Bayesian hierarchical model; Conditionally autoregressive model; Functional data analysis; Joint modeling; Spatial frailty

Recommended Citations

Citations

  • Zhang, J. (2022). Bayesian Hierarchical Modeling for Dependent Data with Applications in Disease Mapping and Functional Data Analysis [Doctoral dissertation, University of Cincinnati]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1649768302824249

    APA Style (7th edition)

  • Zhang, Jieyan. Bayesian Hierarchical Modeling for Dependent Data with Applications in Disease Mapping and Functional Data Analysis. 2022. University of Cincinnati, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=ucin1649768302824249.

    MLA Style (8th edition)

  • Zhang, Jieyan. "Bayesian Hierarchical Modeling for Dependent Data with Applications in Disease Mapping and Functional Data Analysis." Doctoral dissertation, University of Cincinnati, 2022. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1649768302824249

    Chicago Manual of Style (17th edition)

ucin1649768302824249
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This open access ETD is published by University of Cincinnati and OhioLINK.