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Statistics and Computing

, 19:283 | Cite as

Pairwise likelihood estimation for multivariate mixed Poisson models generated by Gamma intensities

  • Florent Chatelain
  • Sophie Lambert-LacroixEmail author
  • Jean-Yves Tourneret
Article

Abstract

Estimating the parameters of multivariate mixed Poisson models is an important problem in image processing applications, especially for active imaging or astronomy. The classical maximum likelihood approach cannot be used for these models since the corresponding masses cannot be expressed in a simple closed form. This paper studies a maximum pairwise likelihood approach to estimate the parameters of multivariate mixed Poisson models when the mixing distribution is a multivariate Gamma distribution. The consistency and asymptotic normality of this estimator are derived. Simulations conducted on synthetic data illustrate these results and show that the proposed estimator outperforms classical estimators based on the method of moments. An application to change detection in low-flux images is also investigated.

Keywords

Pairwise likelihood estimation Multivariate mixed Poisson models Multivariate Gamma distributions Negative multinomial distributions 

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Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  • Florent Chatelain
    • 1
  • Sophie Lambert-Lacroix
    • 2
    Email author
  • Jean-Yves Tourneret
    • 1
  1. 1.IRIT/ENSEEIHT/TésaToulouse Cedex 7France
  2. 2.Laboratoire Jean KuntzmannUniversité de Grenoble et CNRSGrenoble Cedex 9France

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