Open Access
December 2014 Voronoi residual analysis of spatial point process models with applications to California earthquake forecasts
Andrew Bray, Ka Wong, Christopher D. Barr, Frederic Paik Schoenberg
Ann. Appl. Stat. 8(4): 2247-2267 (December 2014). DOI: 10.1214/14-AOAS767


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.


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Andrew Bray. Ka Wong. Christopher D. Barr. Frederic Paik Schoenberg. "Voronoi residual analysis of spatial point process models with applications to California earthquake forecasts." Ann. Appl. Stat. 8 (4) 2247 - 2267, December 2014.


Published: December 2014
First available in Project Euclid: 19 December 2014

zbMATH: 06408777
MathSciNet: MR3292496
Digital Object Identifier: 10.1214/14-AOAS767

Keywords: Epidemic-Type Aftershock Sequence models , Hector Mine , point patterns , residuals analysis , seismology , Voronoi tessellations

Rights: Copyright © 2014 Institute of Mathematical Statistics

Vol.8 • No. 4 • December 2014
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