Spatial point processes: from the mathematical basis to its applications

Abstract

Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2023, Director: Carles Rovira Escofet i Jorge Mateu[en] This work is a study about the spatial point processes. We study the mathematical basis of this object, we expose statistic tools which are used in the analysis of spatial point patterns and, finally, we apply all the exposed theory in a real case study with real data. In the first and second chapter we present the mathematical theory behind the spatial point processes. In the starting chapter we find the most general and abstract definitions, and the very definition of a spatial point process. In this chapter we have used Stoyan et al. 2013 [17]. In the second chapter, using as a reference Diggle 2013 [10], we explain the mathematical theory of the point processes in tha plane. We define and study the properties of several types of processes, and different quantities which are hugely important in the study of this kind of objects. In the third chapter, based mainly in Baddeley et al. (2015) [2], we present, giving examples, the statistic tools used in the analysis of point processes in the plane. The tools exposed are related with the theory exposed previously and are used in the last chapter of the project. Finally, in the last chapter, we put into practice all the knowledge we have acquired in a real case study. Using the database employed in Jorge Mateu, P. Diggle and I. Tamayo-Uria (2014) [18], shared by Jorge Mateu, we perform a study about the rat and cockroach sightings in Madrid city. This constitutes an application in a real public health case of the concepts seen during the work