Using Voronoi tessellations to calculate residuals for spatial point process models

This paper proposes a residual analysis method for spatial point processes where differences between the modeled conditional intensity and the observed number of points are assessed over the Voronoi cells generated by the observations. The resulting residuals are substantially less skewed and more stable than residuals based on a regular grid. These advantages are particularly evident for point processes with conditional intensities close to zero. Performance is compared using simulated data, and an application to models for Southern California earthquakes is provided.