Bayesian analysis of a marked point process: Application in seismic hazard assessment |
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Authors: | Renata Rotondi Elisa Varini |
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Institution: | (1) Istituto Matematica Applicata e Technologie Informatiche, CNR, Via Bassini 15, 20133 Milano, Italy;(2) Università L. Bocconi, Milano, Italy |
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Abstract: | Point processes are the stochastic models most suitable for describing physical phenomena that appear at irregularly spaced
times, such as the earthquakes. These processes are uniquely characterized by their conditional intensity, that is, by the
probability that an event will occur in the infinitesimal interval (t, t+Δt), given the history of the process up tot. The seismic phenomenon displays different behaviours on different time and size scales; in particular, the occurrence of
destructive shocks over some centuries in a seismogenic region may be explained by the elastic rebound theory. This theory
has inspired the so-called stress release models: their conditional intensity translates the idea that an earthquake produces
a sudden decrease in the amount of strain accumulated gradually over time along a fault, and the subsequent event occurs when
the stress exceeds the strength of the medium. This study has a double objective: the formulation of these models in the Bayesian
framework, and the assignment to each event of a mark, that is its magnitude, modelled through a distribution that depends
at timet on the stress level accumulated up to that instant. The resulting parameter space is constrained and dependent on the data,
complicating Bayesian computation and analysis. We have resorted to Monte Carlo methods to solve these problems. |
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Keywords: | Data-constrained parameters Magnitude distribution Metropolis-Hastings algorithm Stress release model |
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