Determinantal point processes (DPPs), which can be dened by their correlation kernels with known moments, are useful models for point patterns where nearby points exhibit repulsion. They have many nice properties, such as closed-form densities, tractable estimation of parameterized families, and no edge eects. In the past, univariate DPPs have been well-studied, both in discrete and continuous settings although their statistical applications are fairly recent and still rather limited, whereas the multivariate DPPs, or the so-called multi-type marked DPPs, have been little explored. In this thesis, we propose a class of multivariate DPPs based on a block kernel construction. For the marked DPP, we show that the conditions of existence of DPP can easily be satised. The block construction allows us to model the individually marked DPPs as well as controlling the scale of repulsion of points having dierent marks. Unlike other researchers who model the kernel function of a DPP, we model its spectral representation, which not only guarantees the existence of the multivariate DPP, but makes the simulation-based estimation methods readily available. In our research, we adopted bivariate complex Fourier basis, which demonstrates nice properties such as constant intensity and approximate isotropy within a short distance between the nearby points. The parameterized block kernels can approximate to commonly-used covariance functions using Fourier expansion. The parameters can be estimated using Maximum Likelihood Estimation, Bayesian approach and Minimum Contrast Estimation. / A Dissertation submitted to the Department of Statistics in partial fulfillment of the requirements for the degree of Doctor of Philosophy. / Spring Semester 2019. / April 17, 2019. / Determinantal Point Processes, DPP, Marked Point Processes, Multivariate DPP, Poisson Processes / Includes bibliographical references. / Fred Huffer, Professor Directing Dissertation; Craig Nolder, University Representative; Xufeng Niu, Committee Member; Jonathan Bradley, Committee Member.
| Identifer | oai:union.ndltd.org:fsu.edu/oai:fsu.digital.flvc.org:fsu_709748 |
| Contributors | Feng, Yiming (author), Nolder, Craig (University Representative), Niu, Xufeng (Committee Member), Bradley, Jonathan R. (Committee Member), Huffer, Fred W. (Fred William) (Professor Directing Dissertation), Florida State University (degree granting institution), College of Arts and Sciences (degree granting college), Department of Statistics (degree granting departmentdgg) |
| Publisher | Florida State University |
| Source Sets | Florida State University |
| Language | English, English |
| Detected Language | English |
| Type | Text, text, doctoral thesis |
| Format | 1 online resource (137 pages), computer, application/pdf |
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