  Many point process models have been proposed for describing and forecasting
earthquake occurrences in seismically active zones such as California, but the
problem of how best to compare and evaluate the goodness of fit of such models
remains open. Existing techniques typically suffer from low power, especially
when used for models with very volatile conditional intensities such as those
used to describe earthquake clusters. This paper proposes a new residual
analysis method for spatial or spatial-temporal point processes involving
inspecting the differences between the modeled conditional intensity and the
observed number of points over the Voronoi cells generated by the observations.
The resulting residuals can be used to construct diagnostic methods of greater
statistical power than residuals based on rectangular grids. Following an
evaluation of performance using simulated data, the suggested method is used to
compare the Epidemic-Type Aftershock Sequence (ETAS) model to the Hector Mine
earthquake catalog. The proposed residuals indicate that the ETAS model with
uniform background rate appears to slightly but systematically underpredict
seismicity along the fault and to overpredict seismicity in along the periphery
of the fault.
