Title: Point patterns in space and space-time: Linear models and change of support
Authors: Jorge Mateu - University Jaume I (Spain) [presenting]
Abstract: Some developments are presented in the theory and applications of point patterns both in space and space-time, focussing in particular in the statistical analysis of linear models for point patterns. We first present some methods for analysing individual effects and their interactions of one or several factors/groups on a set of replicated spatial (possibly marked) and spatio-temporal point patterns. We provide some test statistics based on both the $K$-function and the mark-weighted $K$-function. Since the distributions of our statistics are analytically intractable, we also develop some non-parametric mechanisms for statistical inference. We then present some connections between a spatio-temporal point process and a spatial marked point process by considering a temporal marked point process and a spatial marked one by setting times and locations as marks, respectively. These marked point processes can be explored through several mark summary functions that provide valuable information about the behaviour of the marks and can be used as exploratory quantities that measure the strength and range of interactions between marks. Finally, we have a look at point patterns defined over linear networks opening new avenues of research in this new type of support. We develop new estimators of the first-order intensity function based on both a kernel approach and a Voronoi-based estimator. Applications to real data will be presented.