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An Alternative for the Proportional Hazards Model: Using Accelerated Failure Time Model for the Destructive Earthquake Analysis in Turkey
N. Ata, G. Özel
Abstract
The statistical modeling of destructive earthquakes is an indispensable tool for extracting information from the data on the physics of the earthquake occurrence process, and for making reliable earthquake forecasts. The proportional hazards (PH) model can reveal the seismic activity based on earthquake catalogue. However, if the PH assumption is violated, the PH model should not be used and may entail serious bias and loss of power when estimating or making inference about the effect of parameters. We suggest that accelerated failure time (AFT) model could provide a more suitable description of the earthquake data even when hazards are not proportional. We support this argument using destructive earthquakes occurred in Turkey between 1900 and 2011 having surface wave magnitudes five or more. The PH and AFT models are compared within the context of this data. The evaluation criteria indicate that parametric models are more powerful than the PH model. The data strongly supports that the log-normal AFT model can lead to more precise results than the PH model. The results from this model of seismic events suggest that the possibility of recurrence of a stronger main shock depends on magnitude and stress release of previous main shock.
Keywords
log-normal distribution; non-proportional hazards; parametric survival model; seismic activity.
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