Score, pseudo-score and residual diagnostics for goodness-of-fit of spatial point process models

We develop newtools for formal inference and informalmodel
validation in the analysis of spatial point pattern data. The score test
is generalised to a ‘pseudo-score’ test derived from Besag’s pseudolikelihood,
and to a class of diagnostics based on point process residuals.
The results lend theoretical support to the established practice
of using functional summary statistics such as Ripley’s K-function,
when testing for complete spatial randomness; and they provide new
tools such as the compensator of the K-function for testing other fitted
models. The results also support localisation methods such as the
scan statistic and smoothed residual plots. Software for computing the
diagnostics is provided.