Detecting Randomness on Spatial Point Pattern: A Stat-Geometrical Tool.


  • Prof. Paulo Sérgio Lucio – Investigador Convidado no Centro de Geofísica de Évora – UEVORA
  • FCUL-DEIO – Bloco C/2 – Piso 2 – Sala 2.2.47 – 14:30
  • Quarta-feira, 4 de Dezembro de 2002
In spatial data analysis, the conventional statistical methods cannot be able to detect if the observational units have or do not have a spatial dependence configuration. The spatial pattern analysis treats situations where the observed data set is used in some space domain stochastic process, where the objective is to detect clusters in a point’s domain. The development of methods to describe the spatial configuration of a data set and the possible relationship with other spatial phenomenon are still a challenger. In general, the spatial pattern analysis testifies the Complete Spatial Randomness (CSR) hypothesis against the alternative hypothesis of the data do not present CSR (Regular or Cluster Patterns). There are many tests to detect CSR that do not take into account the neighbourhood information. However it is known that this information is crucial for geology (locations of rock-type), seismology (epicentres of earthquakes), volcanology (locations of craters in a volcanic field), climatology (occurrences of spatial climate extremes), ecology (locations of seedlings in a forest) or sociology (locations of criminality indices). Concerning these fields and several others, the initial exploratory analysis of point patterns frequently requires a reliable test of the CSR hypothesis. This hypothesis states that a homogeneous Poisson process generated the observed spatial pattern. This study deals with sparsely sampled point patterns. Some points are sampled from an ensemble and the spatial pattern is studied through its local properties, in the neighbourhood of the sampled locations. To distinguish the sampled locations or the observed occurrences, from the arbitrary locations composing the ensemble or the population, we call the former events and the latter points. This work aims at presenting an alternative method to the angle test, using both Euclidean and angular distances to verify if they can be used to determine the spatial configuration pattern, allowing a barycentric interpolation of the unsampled points into a simplex two-dimensional (triangular) framework. Under the CSR context, the data set is uniformly distributed in the space domain, and the test using the Kolmogorov-Smirnov statistic, based on the misfit between the empirical and the theoretical distributions, is widely used. In regular configurations, the areas of the triangle network have the tendency to be approximately equals. In clustered configurations, a large number of small areas and a small number of large areas can probably occurs or vice-versa. On the simulations set-up in SPLUS™, the asymptotic test proposed in this study, presents satisfactory results with a high accuracy, accepting the CSR hypothesis when the data has effectively this configuration, and rejecting the CSR otherwise. The power function of the Stat-Geo test was defined, by means structural simulations based on Monte Carlo procedures.