UCLA

This dissertation investigates the strengths and weaknesses of the current methods of residual analysis for spatial point process models. The primary focus is on the manner in which the space should be partitioned to form residuals. It proposes a new method whereby the 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 can be used to construct diagnostic methods of greater statistical power than residuals based on a regular rectangular grid. These advantages are particularly evident for point processes with conditional intensities close to zero, such as those in seismology. Performance is compared using simulated data and applied to models for Southern California earthquakes.