Voronoi residual analysis of spatial point process models with applications to California earthquake forecasts
arXiv:1501.06387 · doi:10.1214/14-AOAS767
Abstract
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.
arXiv commentPublished in at http://dx.doi.org/10.1214/14-AOAS767 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org)
References in corpus (4)
- Assessment of Point Process Models for Earthquake Forecasting
- Residual analysis methods for space--time point processes with applications to earthquake forecast models in California
- Score, Pseudo-Score and Residual Diagnostics for Spatial Point Process Models
- Point process modeling of wildfire hazard in Los Angeles County, California
Cited by in corpus (5)
- A Review of Self-Exciting Spatio-Temporal Point Processes and Their Applications
- Self-exciting point processes with spatial covariates: modeling the dynamics of crime
- Embracing Data Incompleteness for Better Earthquake Forecasting
- Enhancing the statistical evaluation of earthquake forecasts -- An application to Italy
- Comparative evaluation of point process forecasts