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Bayesian Models for Capturing Heterogeneity in Discrete Data

Title: Bayesian Models for Capturing Heterogeneity in Discrete Data.
Name(s): Geng, Junxian, author
Slate, Elizabeth H., professor co-directing dissertation
Pati, Debdeep, professor co-directing dissertation
Schmertmann, Carl P., university representative
Zhang, Xin, (Professor of Engineering), committee member
Florida State University, degree granting institution
College of Arts and Sciences, degree granting college
Department of Statistics , degree granting department
Type of Resource: text
Genre: Text
Doctoral Thesis
Issuance: monographic
Date Issued: 2017
Publisher: Florida State University
Florida State University
Place of Publication: Tallahassee, Florida
Physical Form: computer
online resource
Extent: 1 online resource (98 pages)
Language(s): English
Abstract/Description: Population heterogeneity exists frequently in discrete data. Many Bayesian models perform reasonably well in capturing this subpopulation structure. Typically, the Dirichlet process mixture model (DPMM) and a variable dimensional alternative that we refer to as the mixture of finite mixtures (MFM) model are used, as they both have natural byproducts of clustering derived from Polya urn schemes. The first part of this dissertation focuses on a model for the association between a binary response and binary predictors. The model incorporates Boolean combinations of predictors, called logic trees, as parameters arising from a DPMM or MFM. Joint modeling is proposed to solve the identifiability issue that arises when using a mixture model for a binary response. Different MCMC algorithms are introduced and compared for fitting these models. The second part of this dissertation is the application of the mixture of finite mixtures model to community detection problems. Here, the communities are analogous to the clusters in the earlier work. A probabilistic framework that allows simultaneous estimation of the number of clusters and the cluster configuration is proposed. We prove clustering consistency in this setting. We also illustrate the performance of these methods with simulation studies and discuss applications.
Identifier: FSU_2017SP_Geng_fsu_0071E_13791 (IID)
Submitted Note: A Dissertation submitted to the Department of Statistics in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
Degree Awarded: Spring Semester 2017.
Date of Defense: April 5, 2017.
Keywords: Community Detection, Discrete data, Joint Modeling, MCMC, Mixture Model, Population heterogeneity
Bibliography Note: Includes bibliographical references.
Advisory Committee: Elizabeth H. Slate, Professor Co-Directing Dissertation; Debdeep Pati, Professor Co-Directing Dissertation; Carl P. Schmertmann, University Representative; Xin Zhang, Committee Member.
Subject(s): Statistics
Persistent Link to This Record:
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Host Institution: FSU

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Geng, J. (2017). Bayesian Models for Capturing Heterogeneity in Discrete Data. Retrieved from