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Statistical models and algorithms for large data with complex dependence structures

Li, Miaoqi
http://orcid.org/0000-0002-6686-9046
http://rave.ohiolink.edu/etdc/view?acc_num=ucin1584015958922068

Abstract Details

2020, PhD, University of Cincinnati, Arts and Sciences: Mathematical Sciences.
In this dissertation, our research interest focuses on developing statistical models and algorithms for large-scale data. Specifically, we are considering data with complex dependence structures. Two types of complicated dependence structures have been addressed. They are large-scale network data and multivariate processes with spatial dependence. Network data possess intricate configurations, which causes conducting thorough investigations on properties and making inferences on large-scale networks to be challenged and even infeasible. To overcome these difficulties, we take advantage of recent developments in randomized numerical linear algebra and derive efficient algorithms to estimate the spatial autocorrelation parameter by approximating log likelihood function of the spatial autoregressive (SAR) model. When studying multivariate processes with spatial dependence, we propose a multivariate fused Gaussian process (MFGP) model that is able to flexibly model multivariate spatial processes and enables efficient computation. The proposed model combines a low-rank component and a multivariate Gaussian Markov random field to jointly depict spatial dependence structure that is potentially large-scale, non-stationary and asymmetric. Compelling experimental results from extensive simulation and real data examples demonstrate empirically that the performance and applications of our proposed models and algorithms are better than many state-of-the-art methodologies based on a variety of criteria. The theoretical properties are explored and consistency results are established.
Emily Kang, Ph.D. (Committee Chair)
Won Chang, Ph.D. (Committee Member)
Bledar Konomi, Ph.D. (Committee Member)
Siva Sivaganesan, Ph.D. (Committee Member)
119 p.
Statistics
algorithms; complex dependence structures; large data; statistical models

Recommended Citations

Citations

  • Li, M. (2020). Statistical models and algorithms for large data with complex dependence structures [Doctoral dissertation, University of Cincinnati]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1584015958922068

    APA Style (7th edition)

  • Li, Miaoqi. Statistical models and algorithms for large data with complex dependence structures. 2020. University of Cincinnati, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=ucin1584015958922068.

    MLA Style (8th edition)

  • Li, Miaoqi. "Statistical models and algorithms for large data with complex dependence structures." Doctoral dissertation, University of Cincinnati, 2020. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1584015958922068

    Chicago Manual of Style (17th edition)

ucin1584015958922068
139
© 2020, all rights reserved.
This open access ETD is published by University of Cincinnati and OhioLINK.