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dc.contributor.advisorZhao, Zhigen
dc.creatorLiang, Zhengkang
dc.date.accessioned2022-08-15T19:08:19Z
dc.date.available2022-08-15T19:08:19Z
dc.date.issued2022
dc.identifier.urihttp://hdl.handle.net/20.500.12613/8068
dc.description.abstractIn modern statistical applications when the dimension is relatively large, it is a common practice to reduce the dimension using methods such as principal component analysis (PCA), sliced inverse regression and others before applying any statistical models. In this article, we synthetically combine these two steps by considering three Bayesian multi-index models: Bayesian multi-index additive model (BMIAM) for continuous response variable, Bayesian single-index model for binary response variable, and Bayesian multi-index model for categorical response variable. The indexes are parametrized by the hyper-spherical coordinates. The ridge functions are modeled using the Bayesian B-splines, which could be easily extended to other non-parametric methods. We have shown that the posterior consistency holds under certain conditions for the BMIAM. Further, we have developed the Markov chain Monte Carlo (MCMC) algorithm to sample the posterior of the proposed methods. It has been demonstrated through both simulation and real data analysis that the proposed methods provide a reliable estimation of indexes, dimension reduction space and good predictions for the responses.
dc.format.extent85 pages
dc.language.isoeng
dc.publisherTemple University. Libraries
dc.relation.ispartofTheses and Dissertations
dc.rightsIN COPYRIGHT- This Rights Statement can be used for an Item that is in copyright. Using this statement implies that the organization making this Item available has determined that the Item is in copyright and either is the rights-holder, has obtained permission from the rights-holder(s) to make their Work(s) available, or makes the Item available under an exception or limitation to copyright (including Fair Use) that entitles it to make the Item available.
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/
dc.subjectStatistics
dc.titleOn The Bayesian Multiple Index Models
dc.typeText
dc.type.genreThesis/Dissertation
dc.contributor.committeememberDong, Yuexiao
dc.contributor.committeememberMcalinn, Kenichiro
dc.contributor.committeememberWang, Xiaojing
dc.description.departmentStatistics
dc.relation.doihttp://dx.doi.org/10.34944/dspace/8040
dc.ada.noteFor Americans with Disabilities Act (ADA) accommodation, including help with reading this content, please contact scholarshare@temple.edu
dc.description.degreePh.D.
dc.identifier.proqst14981
dc.date.updated2022-08-11T22:10:06Z
refterms.dateFOA2022-08-15T19:08:20Z
dc.identifier.filenameLiang_temple_0225E_14981.pdf


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