A Deviance Residual for Heterogeneous Spatial Poisson Processes

SUMMARY We present a deviance residual for a spatial heterogeneous Poisson process. The residual is derived from an approximation of the normalising integral of the process. This yields a saturated model estimate of the local intensity at a point, which is the reciprocal of the Dirichlet tile area associated with the point. A number of examples of the use of such a residual in the analysis of spatial point patterns is given.