Bivariate Cox Processes: Some Models for Bivariate Spatial Point Patterns

SUMMARY From certain points of view, the range of probability models currently available for describing the joint behaviour of two point processes is rather limited. In this paper we explore the structure of some further models and apply our results to the statistical analysis of bivariate spatial point patterns. In many branches of science there is interest in the study and description of data which represent the locations of objects as points in an essentially planar region. In the present paper we assume that the objects are of two qualitatively distinguishable types and refer to the data as a bivariate spatial point pattern. A statistical analysis of such data should seek to provide some meaningful summary descriptions of the separate point patterns for each of the two types of object, and of any possible inter-relationship between these two patterns. For example, Fig. 1 shows the locations of 173 newly emergent and 155 1-year-old bramnble 0*~~~~~~ a . A * * tv t * * to~~~~~~~~~~0 , * X *t *.#**. .

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