IDEAS home Printed from https://ideas.repec.org/a/bla/scjsta/v35y2008i3p524-539.html
   My bibliography  Save this article

Bayesian Non‐Parametric Estimation of Smooth Hazard Rates for Seismic Hazard Assessment

Author

Listed:
  • LUCA LA ROCCA

Abstract

. Hazard rate estimation is an alternative to density estimation for positive variables that is of interest when variables are times to event. In particular, it is here shown that hazard rate estimation is useful for seismic hazard assessment. This paper suggests a simple, but flexible, Bayesian method for non‐parametric hazard rate estimation, based on building the prior hazard rate as the convolution mixture of a Gaussian kernel with an exponential jump‐size compound Poisson process. Conditions are given for a compound Poisson process prior to be well‐defined and to select smooth hazard rates, an elicitation procedure is devised to assign a constant prior expected hazard rate while controlling prior variability, and a Markov chain Monte Carlo approximation of the posterior distribution is obtained. Finally, the suggested method is validated in a simulation study, and some Italian seismic event data are analysed.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:scjsta:v:35:y:2008:i:3:p:524-539
    DOI: 10.1111/j.1467-9469.2008.00595.x
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/j.1467-9469.2008.00595.x
    Download Restriction: no
    File URL: https://libkey.io/10.1111/j.1467-9469.2008.00595.x?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
    ---><---

    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.
    2. Hennerfeind, Andrea & Brezger, Andreas & Fahrmeir, Ludwig, 2006. "Geoadditive Survival Models," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1065-1075, September.
    3. P. Ammann, Larry, 1985. "Conditional laplace transforms for bayesian nonparametric inference in reliabity theory," Stochastic Processes and their Applications, Elsevier, vol. 20(2), pages 197-212, September.
    4. Ishwaran, Hemant & James, Lancelot F., 2004. "Computational Methods for Multiplicative Intensity Models Using Weighted Gamma Processes: Proportional Hazards, Marked Point Processes, and Panel Count Data," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 175-190, January.
    5. Luis E. Nieto‐Barajas & Stephen G. Walker, 2002. "Markov Beta and Gamma Processes for Modelling Hazard Rates," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 29(3), pages 413-424, September.
    6. Dani Gamerman, 1991. "Dynamic Bayesian Models for Survival Data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 40(1), pages 63-79, March.
    Full references (including those not matched with items on IDEAS)

    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. Michael L. Pennell & David B. Dunson, 2006. "Bayesian Semiparametric Dynamic Frailty Models for Multiple Event Time Data," Biometrics, The International Biometric Society, vol. 62(4), pages 1044-1052, December.
    2. Antonio Lijoi & Igor Prunster, 2009. "Models beyond the Dirichlet process," Quaderni di Dipartimento 103, University of Pavia, Department of Economics and Quantitative Methods.
    3. Bhattacharjee, Arnab & Bhattacharjee, Madhuchhanda, 2007. "Bayesian Analysis of Hazard Regression Models under Order Restrictions on Covariate Effects and Ageing," MPRA Paper 3938, University Library of Munich, Germany.
    4. Antonio Lijoi & Igor Pruenster & Stephen G. Walker, 2008. "Posterior analysis for some classes of nonparametric models," ICER Working Papers - Applied Mathematics Series 05-2008, ICER - International Centre for Economic Research.
    5. Luping Zhao & Timothy E. Hanson, 2011. "Spatially Dependent Polya Tree Modeling for Survival Data," Biometrics, The International Biometric Society, vol. 67(2), pages 391-403, June.
    6. Thomas A. Murray & Peter F. Thall & Ying Yuan & Sarah McAvoy & Daniel R. Gomez, 2017. "Robust Treatment Comparison Based on Utilities of Semi-Competing Risks in Non-Small-Cell Lung Cancer," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(517), pages 11-23, January.
    7. van Noortwijk, J.M., 2009. "A survey of the application of gamma processes in maintenance," Reliability Engineering and System Safety, Elsevier, vol. 94(1), pages 2-21.
    8. K J Wilson & M Farrow, 2010. "Bayes linear kinematics in the analysis of failure rates and failure time distributions," Journal of Risk and Reliability, , vol. 224(4), pages 309-321, December.
    9. 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.
    10. Cizek, P. & Lei, J. & Ligthart, J.E., 2012. "The Determinants of VAT Introduction : A Spatial Duration Analysis," Other publications TiSEM 835efbcb-4537-4dab-aaa3-c, Tilburg University, School of Economics and Management.
    11. Ian W. McKeague & Mourad Tighiouart, 2000. "Bayesian Estimators for Conditional Hazard Functions," Biometrics, The International Biometric Society, vol. 56(4), pages 1007-1015, December.
    12. Arbel, Julyan & Lijoi, Antonio & Nipoti, Bernardo, 2016. "Full Bayesian inference with hazard mixture models," Computational Statistics & Data Analysis, Elsevier, vol. 93(C), pages 359-372.
    13. Hemant Ishwaran, 2011. "Comments on: Nonparametric inference based on panel count data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(1), pages 48-53, May.
    14. Lancelot F. James, 2005. "Analysis of a Class of Likelihood Based Continuous Time Stochastic Volatility Models including Ornstein-Uhlenbeck Models in Financial Economics," Papers math/0503055, arXiv.org, revised Aug 2005.
    15. Martínez-Ovando Juan Carlos & Walker Stephen G., 2011. "Time-series Modelling, Stationarity and Bayesian Nonparametric Methods," Working Papers 2011-08, Banco de México.
    16. Rui Martins, 2022. "A flexible link for joint modelling longitudinal and survival data accounting for individual longitudinal heterogeneity," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 31(1), pages 41-61, March.
    17. Man-Wai Ho, 2011. "On Bayes inference for a bathtub failure rate via S-paths," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 63(4), pages 827-850, August.
    18. Parfait Munezero, 2022. "Efficient particle smoothing for Bayesian inference in dynamic survival models," Computational Statistics, Springer, vol. 37(2), pages 975-994, April.
    19. 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.
    20. Samuel N. Cohen & Robert J. Elliott, 2013. "Filters and smoothers for self-exciting Markov modulated counting processes," Papers 1311.6257, arXiv.org.

    More about this item

    Statistics

    Access and download statistics

    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:bla:scjsta:v:35:y:2008:i:3:p:524-539. 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: Wiley Content Delivery (email available below). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=0303-6898 .

    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.