Title: New quantitative description for spatial point patterns

An important task of the analysis of spatial point patterns is to examine the dependence between points.   Many summary functions, for example,  the nearest neighbour distance distribution, Ripley's K-function, the empty space function and the periodogram, have been proposed to extract such  information.  One way to assess how good a summary function can capture the dependence structure of a given point pattern is to see how sensitive it will be when it is used to test the complete spatial randomness hypothesis against various alternatives.  A point pattern is said to be completely spatially random if it is a realisation of a stationary Poisson process or a binomial process. Comparative studies, however, suggest that there is no uniformly best test.  In this talk we will introduce new quantitative measures that are more able to detect certain kinds of dependence structure than the existing summary functions.