IDEAS home Printed from https://ideas.repec.org/a/spr/metcap/v12y2010i2d10.1007_s11009-009-9146-2.html
   My bibliography  Save this article

On the Empirical Bayesian Approach for the Poisson-Gaussian Model

Author

Listed:
  • Leonidas Sakalauskas

    (Institute of Mathematics and Informatics)

Abstract

The paper considers numerical issues of the empirical Bayesian approach model, applied to estimation of small rates. The condition for non-singularity of Bayesian estimates is given and the convenient iterative algorithm for estimation is described. The clustering algorithm is also developed, using the property of Poisson-Gaussian model to treat probabilities of events in populations being the same, if the variance of probabilities is small. The approach considered is illustrated by an application to the analysis of homicides and suicides data in Lithuania, 2003–2004.

Suggested Citation

  • Leonidas Sakalauskas, 2010. "On the Empirical Bayesian Approach for the Poisson-Gaussian Model," Methodology and Computing in Applied Probability, Springer, vol. 12(2), pages 247-259, June.
    • Handle: RePEc:spr:metcap:v:12:y:2010:i:2:d:10.1007_s11009-009-9146-2
    DOI: 10.1007/s11009-009-9146-2
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11009-009-9146-2
    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/s11009-009-9146-2?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. Leite, José G. & Rodrigues, Josemar & Milan, Luis A., 2000. "A Bayesian analysis for estimating the number of species in a population using nonhomogeneous Poisson process," Statistics & Probability Letters, Elsevier, vol. 48(2), pages 153-161, June.
    2. Quigley, John & Bedford, Tim & Walls, Lesley, 2007. "Estimating rate of occurrence of rare events with empirical bayes: A railway application," Reliability Engineering and System Safety, Elsevier, vol. 92(5), pages 619-627.
    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. Jakimauskas, Gintautas & Sakalauskas, Leonidas, 2016. "Note on the singularity of the Poisson–gamma model," Statistics & Probability Letters, Elsevier, vol. 114(C), pages 86-92.
    2. Audrius Kabašinskas & Leonidas Sakalauskas & Ingrida Vaičiulytė, 2021. "An Analytical EM Algorithm for Sub-Gaussian Vectors," Mathematics, MDPI, vol. 9(9), pages 1-20, April.

    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. Xie, Shuyi & Huang, Zimeng & Wu, Gang & Luo, Jinheng & Li, Lifeng & Ma, Weifeng & Wang, Bohong, 2024. "Combining precursor and Cloud Leaky noisy-OR logic gate Bayesian network for dynamic probability analysis of major accidents in the oil depots," Reliability Engineering and System Safety, Elsevier, vol. 241(C).
    2. Maalouf, Maher & Trafalis, Theodore B., 2011. "Robust weighted kernel logistic regression in imbalanced and rare events data," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 168-183, January.
    3. Quigley, John & Walls, Lesley & Demirel, Güven & MacCarthy, Bart L. & Parsa, Mahdi, 2018. "Supplier quality improvement: The value of information under uncertainty," European Journal of Operational Research, Elsevier, vol. 264(3), pages 932-947.
    4. Norrington, Lisa & Quigley, John & Russell, Ashley & Van der Meer, Robert, 2008. "Modelling the reliability of search and rescue operations with Bayesian Belief Networks," Reliability Engineering and System Safety, Elsevier, vol. 93(7), pages 940-949.
    5. Nima Khakzad & Sina Khakzad & Faisal Khan, 2014. "Probabilistic risk assessment of major accidents: application to offshore blowouts in the Gulf of Mexico," 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. 74(3), pages 1759-1771, December.
    6. Quigley, John & Walls, Lesley, 2011. "Mixing Bayes and empirical Bayes inference to anticipate the realization of engineering concerns about variant system designs," Reliability Engineering and System Safety, Elsevier, vol. 96(8), pages 933-941.
    7. Beverley Causey, 2002. "Parametric estimation of the number of classes in a population," Journal of Applied Statistics, Taylor & Francis Journals, vol. 29(6), pages 925-934.
    8. Keisuke Himoto, 2020. "Hierarchical Bayesian Modeling of Post‐Earthquake Ignition Probabilities Considering Inter‐Earthquake Heterogeneity," Risk Analysis, John Wiley & Sons, vol. 40(6), pages 1124-1138, June.
    9. John Quigley & Kevin J. Wilson & Lesley Walls & Tim Bedford, 2013. "A Bayes Linear Bayes Method for Estimation of Correlated Event Rates," Risk Analysis, John Wiley & Sons, vol. 33(12), pages 2209-2224, December.
    10. Hongyang Yu & Faisal Khan & Brian Veitch, 2017. "A Flexible Hierarchical Bayesian Modeling Technique for Risk Analysis of Major Accidents," Risk Analysis, John Wiley & Sons, vol. 37(9), pages 1668-1682, September.
    11. Quigley, John & Hardman, Gavin & Bedford, Tim & Walls, Lesley, 2011. "Merging expert and empirical data for rare event frequency estimation: Pool homogenisation for empirical Bayes models," Reliability Engineering and System Safety, Elsevier, vol. 96(6), pages 687-695.
    12. Khakzad, Nima & Khan, Faisal & Paltrinieri, Nicola, 2014. "On the application of near accident data to risk analysis of major accidents," Reliability Engineering and System Safety, Elsevier, vol. 126(C), pages 116-125.
    13. Nima Khakzad & Faisal Khan & Paul Amyotte, 2015. "Major Accidents (Gray Swans) Likelihood Modeling Using Accident Precursors and Approximate Reasoning," Risk Analysis, John Wiley & Sons, vol. 35(7), pages 1336-1347, July.

    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:metcap:v:12:y:2010:i:2:d:10.1007_s11009-009-9146-2. 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.