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On the Empirical Bayesian Approach for the Poisson-Gaussian Model

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  • 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
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    References listed on IDEAS

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    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.
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    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.

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