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Modern, powerful techniques for the residual analysis of spatial-temporalpoint process models are reviewed and compared. These methods are applied toCalifornia earthquake forecast models used in the Collaboratory for the Studyof Earthquake Predictability (CSEP). Assessments of these earthquakeforecasting models have previously been performed using simple, low-power meanssuch as the L-test and N-test. We instead propose residual methods based onrescaling, thinning, superposition, weighted K-functions and devianceresiduals. Rescaled residuals can be useful for assessing the overall fit of amodel, but as with thinning and superposition, rescaling is generallyimpractical when the conditional intensity $\lambda$ is volatile. Whileresidual thinning and superposition may be useful for identifying spatiallocations where a model fits poorly, these methods have limited power when themodeled conditional intensity assumes extremely low or high values somewhere inthe observation region, and this is commonly the case for earthquakeforecasting models. A recently proposed hybrid method of thinning andsuperposition, called super-thinning, is a more powerful alternative.

Residual analysis methods for space--time point processes with applications to earthquake forecast models in California