A0363
Title: A roughness penalty approach for time-evolving occurrences on planar and curved regions
Authors: Blerta Begu - University College Dublin (Italy) [presenting]
Abstract: The purpose is to address space-time point processes and analyze their continuous evolution across both spatial and temporal dimensions. An innovative nonparametric methodology is introduced to estimate the unknown space-time density of point patterns or, equivalently, the intensity of an inhomogeneous space-time Poisson point process. The approach combines maximum likelihood estimation with roughness penalties, leveraging differential operators across spatial and temporal domains. Key theoretical properties of the estimator are first established, including consistency. Subsequently, an efficient and flexible estimation procedure is developed, utilizing advanced numerical and computational techniques. By employing finite elements for spatial discretization and B-splines for temporal discretization, the method can effectively model complex, multi-modal, and strongly anisotropic spatiotemporal point patterns. These patterns can be observed over planar or curved domains with intricate geometries, such as coastal regions with complicated shorelines or curved regions with complex orography. Beyond estimation, the method includes tools for appropriate uncertainty quantification. The proposed method is validated through simulation studies and applications to real-world data, demonstrating significant advantages over existing state-of-the-art approaches.
