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Activity Number:
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386
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Type:
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Contributed
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Date/Time:
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Wednesday, August 1, 2007 : 8:30 AM to 10:20 AM
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Sponsor:
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Section on Statistics and the Environment
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| Abstract - #309945 |
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Title:
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Bias in the Estimation of Self-Exciting Point Process Models for Earthquake Occurrences
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Author(s):
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Annie Chu*+ and Frederic Paik Schoenberg and Alejandro Veen
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Companies:
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University of California, Los Angeles and University of California, Los Angeles and IBM T.J. Watson Research Center
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Address:
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8117 Math Science Building, Los Angeles, CA, 90095-1554,
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Keywords:
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earthquakes ; epidemic-type aftershock sequence models ; ETAS models ; space-time point process models ; branching process models ; bias in MLE
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Abstract:
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The space-time Epidemic-Type Aftershock Sequence (ETAS) model developed by Ogata (1998) is a branching point process model having been successfully used to characterize certain earthquake catalogs. However, many modern earthquake catalogs are missing many events, especially those of small magnitude. Hence most analyses institute a lower magnitude threshold before fitting a model such as ETAS. The impact of the magnitude cutoff on the branching ratio has been investigated by Sornette and Werner (2005). We investigate the impact of the magnitude threshold on the bias in maximum likelihood estimates of the parameters in the ETAS model. Our investigations make repeated use of an EM method to obtain stable MLE for branching point process models, developed by Veen (2006). Results are demonstrated with simulations and use a catalog compiled by the Southern California Earthquake Center (SCEC).
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