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Recursions on the marginals and exact computation of the normalizing constant for Gibbs processes

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  • Cécile Hardouin
  • Xavier Guyon

Abstract

This paper presents different recursive formulas for computing the marginals and the normalizing constant of a Gibbs distribution $$\pi $$ π . The common thread is the use of the underlying Markov properties of such processes. The procedures are illustrated with several examples, particularly the Ising model. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • Cécile Hardouin & Xavier Guyon, 2014. "Recursions on the marginals and exact computation of the normalizing constant for Gibbs processes," Computational Statistics, Springer, vol. 29(6), pages 1637-1650, December.
    • Handle: RePEc:spr:compst:v:29:y:2014:i:6:p:1637-1650
    DOI: 10.1007/s00180-014-0510-5
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    References listed on IDEAS

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    1. R. Reeves, 2004. "Efficient recursions for general factorisable models," Biometrika, Biometrika Trust, vol. 91(3), pages 751-757, September.
    2. A. N. Pettitt & N. Friel & R. Reeves, 2003. "Efficient calculation of the normalizing constant of the autologistic and related models on the cylinder and lattice," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(1), pages 235-246, February.
    3. J. Møller & A. N. Pettitt & R. Reeves & K. K. Berthelsen, 2006. "An efficient Markov chain Monte Carlo method for distributions with intractable normalising constants," Biometrika, Biometrika Trust, vol. 93(2), pages 451-458, June.
    4. Francesco Bartolucci, 2002. "A recursive algorithm for Markov random fields," Biometrika, Biometrika Trust, vol. 89(3), pages 724-730, August.
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