Second-order residual analysis of spatiotemporal point processes and applications in model evaluation
Journal of the Royal Statistical Society: Series B (Statistical Methodology) · 2006 · Volume 68 · Issue 4
DOI: 10.1111/j.1467-9868.2006.00559.x
Abstract
Summary.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
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