IDEAS home Printed from https://ideas.repec.org/a/spr/stmapp/v12y2003i1d10.1007_bf02511585.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/BF02511585
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/BF02511585?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Vere-Jones, David, 1995. "Forecasting earthquakes and earthquake risk," International Journal of Forecasting, Elsevier, vol. 11(4), pages 503-538, December.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Chenlong Li & Zhanjie Song & Wenjun Wang, 2020. "Space–time inhomogeneous background intensity estimators for semi-parametric space–time self-exciting point process models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(4), pages 945-967, August.
    2. Schneider, Michael & Lillo, Fabrizio & Pelizzon, Loriana, 2016. "How has sovereign bond market liquidity changed? An illiquidity spillover analysis," SAFE Working Paper Series 151, Leibniz Institute for Financial Research SAFE.
    3. Samuel N. Cohen & Robert J. Elliott, 2013. "Filters and smoothers for self-exciting Markov modulated counting processes," Papers 1311.6257, arXiv.org.
    4. Ericsson, Neil R., 2017. "How biased are U.S. government forecasts of the federal debt?," International Journal of Forecasting, Elsevier, vol. 33(2), pages 543-559.
    5. Tsai, Chung-Hung & Chen, Cheng-Wu, 2011. "The establishment of a rapid natural disaster risk assessment model for the tourism industry," Tourism Management, Elsevier, vol. 32(1), pages 158-171.
    6. Luca La Rocca, 2008. "Bayesian Non‐Parametric Estimation of Smooth Hazard Rates for Seismic Hazard Assessment," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 35(3), pages 524-539, September.
    7. Altay, Nezih & Narayanan, Arunachalam, 2022. "Forecasting in humanitarian operations: Literature review and research needs," International Journal of Forecasting, Elsevier, vol. 38(3), pages 1234-1244.
    8. Roelof Helmers & Ričardas Zitikis, 1999. "On Estimation of Poisson Intensity Functions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 51(2), pages 265-280, June.
    9. Tsai, Chung-Hung & Chen, Cheng-Wu, 2010. "An earthquake disaster management mechanism based on risk assessment information for the tourism industry-a case study from the island of Taiwan," Tourism Management, Elsevier, vol. 31(4), pages 470-481.
    10. Nikolopoulos, Konstantinos & Petropoulos, Fotios & Rodrigues, Vasco Sanchez & Pettit, Stephen & Beresford, Anthony, 2022. "A disaster response model driven by spatial–temporal forecasts," International Journal of Forecasting, Elsevier, vol. 38(3), pages 1214-1220.
    11. Bent Natvig & Ingunn Fride Tvete, 2007. "Bayesian Hierarchical Space–time Modeling of Earthquake Data," Methodology and Computing in Applied Probability, Springer, vol. 9(1), pages 89-114, March.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:stmapp:v:12:y:2003:i:1:d:10.1007_bf02511585. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.