We develop new tools for formal inference and informal model validation in the analysis of spatial point pattern data. The score test is generalized to a “pseudo-score” test derived from Besag’s pseudo-likelihood, 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 localization methods such as the scan statistic and smoothed residual plots. Software for computing the diagnostics is provided.
"Score, Pseudo-Score and Residual Diagnostics for Spatial Point Process Models." Statist. Sci. 26 (4) 613 - 646, November 2011. https://doi.org/10.1214/11-STS367