Maximum likelihood estimations in a nonlinear self-exciting point process model

1986 ◽  
Vol 55 (4) ◽  
pp. 219-225 ◽  
Author(s):  
H. van den Boogaard
Keyword(s):  
Maximum Likelihood ◽  
Point Process ◽  
Process Model ◽  
Point Process Model ◽  
Maximum Likelihood Estimations

scholarly journals A stochastic marked point process model for earthquakes

2003 ◽  
Vol 3 (1/2) ◽  
pp. 95-101 ◽  
Author(s):  
L. Holden ◽  
S. Sannan ◽  
H. Bungum
Keyword(s):  
Maximum Likelihood ◽  
Stochastic Model ◽  
Point Process ◽  
Process Model ◽  
Marked Point ◽  
Marked Point Process ◽  
Earthquake Occurrence ◽  
Point Process Model ◽  
Spatio Temporal ◽  
Temporal Interactions

Abstract. A simplified stochastic model for earthquake occurrence focusing on the spatio-temporal interactions between earthquakes is presented. The model is a marked point process model in which each earthquake is represented by its magnitude and coordinates in space and time. The model incorporates the occurrence of aftershocks as well as the build-up and subsequent release of strain. The parameters of the model are estimated from a maximum likelihood calculation.

Exploratory analysis of earthquake clusters by likelihood-based trigger models

2001 ◽  
Vol 38 (A) ◽  
pp. 202-212 ◽  
Author(s):  
Yosihiko Ogata
Keyword(s):  
Maximum Likelihood ◽  
Point Process ◽  
Process Model ◽  
Intensity Function ◽  
Exploratory Analysis ◽  
Maximum Likelihood Estimates ◽  
Conditional Intensity ◽  
Point Process Model ◽  
Conditional Intensity Function ◽  
Earthquake Clusters

The paper considers the superposition of modified Omori functions as a conditional intensity function for a point process model used in the exploratory analysis of earthquake clusters. For the examples discussed, the maximum likelihood estimates converge well starting from appropriate initial values even though the number of parameters estimated can be large (though never larger than the number of observations). Three datasets are subjected to different analyses, showing the use of the model to discover and study individual clustering features.

Exploratory analysis of earthquake clusters by likelihood-based trigger models

2001 ◽  
Vol 38 (A) ◽  
pp. 202-212 ◽  
Author(s):  
Yosihiko Ogata
Keyword(s):  
Maximum Likelihood ◽  
Point Process ◽  
Process Model ◽  
Intensity Function ◽  
Exploratory Analysis ◽  
Maximum Likelihood Estimates ◽  
Conditional Intensity ◽  
Point Process Model ◽  
Conditional Intensity Function ◽  
Earthquake Clusters

The paper considers the superposition of modified Omori functions as a conditional intensity function for a point process model used in the exploratory analysis of earthquake clusters. For the examples discussed, the maximum likelihood estimates converge well starting from appropriate initial values even though the number of parameters estimated can be large (though never larger than the number of observations). Three datasets are subjected to different analyses, showing the use of the model to discover and study individual clustering features.

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