Application of hidden semi-Markov models for the seismic hazard assessment of the North and South Aegean Sea, Greece

The real stress field in an area associated with earthquake generation cannot be directly observed. For that purpose we apply hidden semi-Markov models (HSMMs) for strong earthquake occurrence in the areas of North and South Aegean Sea considering that the stress field constitutes the hidden process...

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Published in:Journal of applied statistics Vol. 44; no. 6; pp. 1064 - 1085
Main Authors: Pertsinidou, C. E., Tsaklidis, G., Papadimitriou, E., Limnios, N.
Format: Journal Article
Language:English
Published: Abingdon Taylor & Francis 26.04.2017
Taylor & Francis Ltd
Taylor & Francis (Routledge)
Subjects:
Aegean sea
Algorithms
Applied statistics
Assessments
Earthquakes
EM algorithm
Hidden semi-Markov model
Markov analysis
Markov models
Mathematical models
Mathematics
Parameter estimation
Seismic hazard
Statistics
stress field
Stresses
Viterbi-decoding algorithm
ISSN:0266-4763, 1360-0532
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Abstract The real stress field in an area associated with earthquake generation cannot be directly observed. For that purpose we apply hidden semi-Markov models (HSMMs) for strong earthquake occurrence in the areas of North and South Aegean Sea considering that the stress field constitutes the hidden process. The advantage of HSMMs compared to hidden Markov models (HMMs) is that they allow any arbitrary distribution for the sojourn times. Poisson, Logarithmic and Negative Binomial distributions as well as different model dimensions are tested. The parameter estimation is achieved via the EM algorithm. For the decoding procedure, a new Viterbi algorithm with a simple form is applied detecting precursory phases (hidden stress variations) and warning for anticipated earthquake occurrences. The optimal HSMM provides an alarm period for 70 out of 88 events. HMMs are also studied presenting poor results compared to these obtained via HSMMs. Bootstrap standard errors and confidence intervals for the parameters are evaluated and the forecasting ability of the Poisson models is examined.
AbstractList The real stress field in an area associated with earthquake generation cannot be directly observed. For that purpose we apply hidden semi-Markov models (HSMMs) for strong earthquake occurrence in the areas of North and South Aegean Sea considering that the stress field constitutes the hidden process. The advantage of HSMMs compared to hidden Markov models (HMMs) is that they allow any arbitrary distribution for the sojourn times. Poisson, Logarithmic and Negative Binomial distributions as well as different model dimensions are tested. The parameter estimation is achieved via the EM algorithm. For the decoding procedure, a new Viterbi algorithm with a simple form is applied detecting precursory phases (hidden stress variations) and warning for anticipated earthquake occurrences. The optimal HSMM provides an alarm period for 70 out of 88 events. HMMs are also studied presenting poor results compared to these obtained via HSMMs. Bootstrap standard errors and confidence intervals for the parameters are evaluated and the forecasting ability of the Poisson models is examined.
The real stress field in an area associated with earthquake generation cannot be directly observed. For that purpose we apply hidden semi-Markov models (HSMMs) for strong [Formula omitted.] earthquake occurrence in the areas of North and South Aegean Sea considering that the stress field constitutes the hidden process. The advantage of HSMMs compared to hidden Markov models (HMMs) is that they allow any arbitrary distribution for the sojourn times. Poisson, Logarithmic and Negative Binomial distributions as well as different model dimensions are tested. The parameter estimation is achieved via the EM algorithm. For the decoding procedure, a new Viterbi algorithm with a simple form is applied detecting precursory phases (hidden stress variations) and warning for anticipated earthquake occurrences. The optimal HSMM provides an alarm period for 70 out of 88 events. HMMs are also studied presenting poor results compared to these obtained via HSMMs. Bootstrap standard errors and confidence intervals for the parameters are evaluated and the forecasting ability of the Poisson models is examined.
The real stress field in an area associated with earthquake generation cannot be directly observed. For that purpose we apply hidden semi-Markov models (HSMMs) for strong [Image omitted.] earthquake occurrence in the areas of North and South Aegean Sea considering that the stress field constitutes the hidden process. The advantage of HSMMs compared to hidden Markov models (HMMs) is that they allow any arbitrary distribution for the sojourn times. Poisson, Logarithmic and Negative Binomial distributions as well as different model dimensions are tested. The parameter estimation is achieved via the EM algorithm. For the decoding procedure, a new Viterbi algorithm with a simple form is applied detecting precursory phases (hidden stress variations) and warning for anticipated earthquake occurrences. The optimal HSMM provides an alarm period for 70 out of 88 events. HMMs are also studied presenting poor results compared to these obtained via HSMMs. Bootstrap standard errors and confidence intervals for the parameters are evaluated and the forecasting ability of the Poisson models is examined.
Author Papadimitriou, E.
Limnios, N.
Pertsinidou, C. E.
Tsaklidis, G.
Author_xml – sequence: 1
  givenname: C. E.
  surname: Pertsinidou
  fullname: Pertsinidou, C. E.
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  fullname: Tsaklidis, G.
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  surname: Papadimitriou
  fullname: Papadimitriou, E.
  organization: Department of Geophysics, Aristotle University of Thessaloniki
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  surname: Limnios
  fullname: Limnios, N.
  organization: LMAC Laboratoire de Mathématiques Appliquées de Compiègne EA2222, Sorbonne universités, Université de Technologie de Compiègne -CS
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Snippet The real stress field in an area associated with earthquake generation cannot be directly observed. For that purpose we apply hidden semi-Markov models (HSMMs)...
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SubjectTerms Aegean sea
Algorithms
Applied statistics
Assessments
Earthquakes
EM algorithm
Hidden semi-Markov model
Markov analysis
Markov models
Mathematical models
Mathematics
Parameter estimation
Seismic hazard
Statistics
stress field
Stresses
Viterbi-decoding algorithm
Title Application of hidden semi-Markov models for the seismic hazard assessment of the North and South Aegean Sea, Greece
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