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Bayesian analysis of a marked point process: Application in seismic hazard assessment

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  • Renata Rotondi

    (CNR)

  • Elisa Varini

    (Università L. Bocconi)

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.

Suggested Citation

  • Renata Rotondi & Elisa Varini, 2003. "Bayesian analysis of a marked point process: Application in seismic hazard assessment," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 12(1), pages 79-92, February.
    • Handle: RePEc:spr:stmapp:v:12:y:2003:i:1:d:10.1007_bf02511585
    DOI: 10.1007/BF02511585
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    References listed on IDEAS

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    1. Vere-Jones, David, 1995. "Forecasting earthquakes and earthquake risk," International Journal of Forecasting, Elsevier, vol. 11(4), pages 503-538, December.
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    Cited by:

    1. Elliott, Robert & Limnios, Nikolaos & Swishchuk, Anatoliy, 2013. "Filtering hidden semi-Markov chains," Statistics & Probability Letters, Elsevier, vol. 83(9), pages 2007-2014.
    2. Ye Zheng & Yazhou Xie & Xuejiao Long, 2021. "A comprehensive review of Bayesian statistics in natural hazards engineering," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 108(1), pages 63-91, August.

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