New Development in Point Process Theory, Methods and Applications

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With the rapid development of modern data collection technologies, high-resolution spatial, temporal, and spatial-temporal data have become available at an unprecedented speed in recent years. The complexity and magnitude of these new data call for new statistical modeling tools. The proposed research will develop new modeling tools that can be used to analyze complex and large data. Novel applications of the proposed methods will be considered to answer scientific questions arising in disciplines such as epidemiology, finance, and sociology.This project will develop new theory and methods in point processes. In particular, the project will develop (1) more efficient estimation procedures based on quasi-likelihood to fit point process models and (2) a novel framework to conduct principle component analysis for marked point processes. For the first aim, efficient computational algorithms will be developed and theoretical properties of these algorithms will be investigated. For the second aim, the marks and points of the marked point process are linked through two potentially correlated latent processes, and principle component analysis is conducted for each of the two latent processes. Theoretical properties of the proposed method will be investigated. Data driven procedures will be developed to select the tuning parameters.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.