Estimation of Space-Time Branching Process Models in Seismology Using an EM-Type Algorithm

Maximum likelihood estimation of branching point process models via numerical optimization procedures can be unstable and computationally intensive. We explore an alternative estimation method based on the expectation-maximization algorithm. The method involves viewing the estimation of such branchi...

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Vydáno v:	Journal of the American Statistical Association Ročník 103; číslo 482; s. 614 - 624
Hlavní autoři:	Veen, Alejandro, Schoenberg, Frederic P
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Alexandria, VA Taylor & Francis 01.06.2008 American Statistical Association Taylor & Francis Ltd
Témata:	Algorithms Applications Applications and Case Studies Branching process models Disease models Earthquakes Epidemic-type aftershock sequence model Epidemiology Estimate reliability Estimating techniques Estimation Estimation bias Exact sciences and technology Expectation-maximization algorithm General topics Geology Markov processes Mathematics Maximum likelihood Maximum likelihood estimation Maximum likelihood method Modeling Optimization Parametric inference Probability and statistics Probability theory and stochastic processes Regions Regression analysis Robustness (mathematics) Sciences and techniques of general use Seismicity Seismology Simulations Space-time point process models Spacetime Statistical methods Statistics Stochastic processes Tree structures United States > US Southern California Expectation-maximization algorithm Epidemic-type aftershock sequence model Covering problem Optimization method Optimization Hypothesis test Statistical test Branching process models Earthquakes Log likelihood Incomplete information Likelihood function Mathematical programming Epidemic Maximization Numerical model Space time Statistical method Space-time point process models Branching process Numerical analysis Point estimation Point process Maximum likelihood Expectation EM algorithm Application
ISSN:	0162-1459, 1537-274X
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Shrnutí:	Maximum likelihood estimation of branching point process models via numerical optimization procedures can be unstable and computationally intensive. We explore an alternative estimation method based on the expectation-maximization algorithm. The method involves viewing the estimation of such branching processes as analogous to incomplete data problems. Using an application from seismology, we show how the epidemic-type aftershock sequence (ETAS) model can, in fact, be estimated this way, and we propose a computationally efficient procedure to maximize the expected complete data log-likelihood function. Using a space-time ETAS model, we demonstrate that this method is extremely robust and accurate and use it to estimate declustered background seismicity rates of geologically distinct regions in Southern California. All regions show similar declustered background intensity estimates except for the one covering the southern section of the San Andreas fault system to the east of San Diego in which a substantially higher intensity is observed.
Bibliografie:	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 ObjectType-Feature-1 ObjectType-Article-2 content type line 23
ISSN:	0162-1459 1537-274X
DOI:	10.1198/016214508000000148