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

• 成果类型: Article
• 署名作者: Zhuang, Jiancang
• 署名单位: Research Organization of Information & Systems (ROIS); Institute of Statistical Mathematics (ISM) - Japan
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1111/j.1467-9868.2006.00559.x
• 发表日期: 2006
• 页码: 635-653
• 关键词: triggered seismicity; earthquake; aftershocks; foreshocks

摘要

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.