Voronoi residual analysis of spatial point process models with applications to California earthquake forecasts

TL;DR

This paper introduces a Voronoi residual analysis method for spatial point process models, improving goodness-of-fit evaluation for earthquake forecasts by providing more powerful diagnostics than traditional grid-based residuals.

Contribution

It proposes a novel Voronoi-based residual analysis technique for spatial point processes, enhancing model diagnostics especially for volatile earthquake models.

Findings

Voronoi residuals outperform grid-based residuals in power.

Application to California earthquake data reveals model underprediction along faults.

ETAS model shows systematic biases in seismicity prediction.

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.