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Second‐order residual analysis of spatiotemporal point processes and applications in model evaluation
Author(s) -
Zhuang Jiancang
Publication year - 2006
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/j.1467-9868.2006.00559.x
Subject(s) - residual , point (geometry) , computer science , point process , order (exchange) , algorithm , mathematics , statistics , geometry , finance , economics
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.