Proposta de um teste para verificar a hipótese de independência entre pontos e marcas quantitativas de um processo pontual marcado em rede linear

Abstract

To analyze marked point processes it is necessary to assume that observations (that is, marks) and locations (that is, points) are dependents. There are several available methods to test the validity of this assumption in the plan. However, there are no statistical tests available in the literature with this purpose in case of the observations are located in a network (e.g. rivers, streets, etc). In this thesis, it is proposed a formal approach to test this assumption. The test is based on two characteristics (E(t) and V(t)) of stationary and isotropic marked point processes in the plane that were proposed by Schlather, Ribeiro e Diggle (2004). These quantities are functions of the distance t between points and denote the expectation and conditional variance, respectively, of a mark given that there is another point of the point process at a distance t. In this thesis, we adapted the independence test between quantitative marks and points proposed by Schlather, Ribeiro e Diggle (2004) for the case of linear networks. The test was evaluated through Monte Carlo simulations and applied in actual data of the diameter at breast height (DBH) of trees of the species Heura Crepitans located on the banks of the rivers that cross the Fazenda Canary located in the state of Acre, Brazil. The results show that the proposed test may be useful in detecting dependence between quantitative marks and points of marked point processes in linear networks.