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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Bibliographic Details
Published in:Journal of the American Statistical Association Vol. 103; no. 482; pp. 614 - 624
Main Authors: Veen, Alejandro, Schoenberg, Frederic P
Format: Journal Article
Language:English
Published: Alexandria, VA Taylor & Francis 01.06.2008
American Statistical Association
Taylor & Francis Ltd
Subjects:
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
Online Access:Get full text
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Description
Summary: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.
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ISSN:0162-1459
1537-274X
DOI:10.1198/016214508000000148