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    On The Bayesian Multiple Index Models

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    Genre
    Thesis/Dissertation
    Date
    2022
    Author
    Liang, Zhengkang
    Advisor
    Zhao, Zhigen
    Committee member
    Dong, Yuexiao
    Mcalinn, Kenichiro
    Wang, Xiaojing
    Department
    Statistics
    Subject
    Statistics
    Permanent link to this record
    http://hdl.handle.net/20.500.12613/8068
    
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    DOI
    http://dx.doi.org/10.34944/dspace/8040
    Abstract
    In 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.
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