Second-order residual analysis of spatiotemporal point processes and applications in model evaluation

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The paper gives first-order residual analysis for spatiotemporal point processes that is similar to the residual analysis that has been developed by Baddeley and co-workers for spatial point processes and also proposes principles for second-order residual analysis based on the viewpoint of martingales. Examples are given for both first- and second-order residuals. In particular, residual analysis can be used as a powerful tool in model improvement. Taking a spatiotemporal epidemic-type aftershock sequence model for earthquake occurrences as the base-line model, second-order residual analysis can be useful for identifying many features of the data that are not implied in the base-line model, providing us with clues about how to formulate better models.

Keywords: Earthquake clusters; Epidemic-type aftershock sequence model; Martingale; Model evaluation; Point process; Residual analysis

Document Type: Research Article


Affiliations: Institute of Statistical Mathematics, Tokyo, Japan

Publication date: September 1, 2006

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