Publications

Description

Authors: Blerta Begu, Simone Panzeri, Eleonora Arnone, Michelle Carey, Laura M. Sangalli

Abstract: In this work, we consider space–time point processes and study their continuous space–time evolution. We propose an innovative nonparametric methodology to estimate the unknown space–time density of the point pattern, or, equivalently, to estimate the intensity of an inhomogeneous space–time Poisson point process. The presented approach combines (opens in a new window)maximum likelihood estimation with roughness penalties, based on differential operators, defined over the spatial and temporal domains of interest. We first establish some important theoretical properties of the considered estimator, including its consistency. We then develop an efficient and flexible estimation procedure that leverages advanced numerical and computation techniques. Thanks to a (opens in a new window)discretization based on (opens in a new window)finite elements in space and B-splines in time, the proposed method can effectively capture complex multi-modal and strongly (opens in a new window)anisotropic spatio-temporal point patterns; moreover, these point patterns may be observed over planar or curved domains with non-trivial geometries, due to geographic constraints, such as coastal regions with complicated shorelines, or curved regions with complex (opens in a new window)orography. In addition to providing estimates, the method’s functionalities also include the introduction of appropriate (opens in a new window)uncertainty quantification tools. We thoroughly validate the proposed method, by means of simulation studies and applications to real-world data. The obtained results highlight significant advantages over state-of-the-art competing approaches.