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A cluster identification framework illustrated by a filtering model for earthquake occurrences. (English) Zbl 1204.62163

Summary: A general dynamical cluster identification framework including both modeling and computation is developed. The earthquake declustering problem is studied to demonstrate how this framework applies. A stochastic model is proposed for earthquake occurrences that considers the sequence of occurrences as composed of two parts: earthquake clusters and single earthquakes. We suggest that earthquake clusters contain a “mother quake” and her “offspring”. Applying the filtering techniques, we use the solution of filtering equations as criteria for declustering. A procedure for calculating maximum likelihood estimations (MLE’s) and the most likely cluster sequence is also presented.

MSC:

62M20 Inference from stochastic processes and prediction
62P99 Applications of statistics
86A17 Global dynamics, earthquake problems (MSC2010)
62M09 Non-Markovian processes: estimation
60G55 Point processes (e.g., Poisson, Cox, Hawkes processes)

Software:

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References:

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