Comptes Rendus
Statistics
Exact marginals and normalizing constant for Gibbs distributions
Comptes Rendus. Mathématique, Volume 348 (2010) no. 3-4, pp. 199-201.

We present a recursive algorithm for the calculation of the marginal of a Gibbs distribution π. A direct consequence is the calculation of the normalizing constant of π.

Nous proposons dans ce travail une récurrence sur les lois marginales d'une distribution de Gibbs π. Une conséquence directe est le calcul exact de la constante de normalisation de π.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2009.12.002

Cécile Hardouin 1; Xavier Guyon 1

1 CES/SAMOS-MATISSE/Université de Paris, 190, rue de Tolbiac, 75634 Paris cedex 13, France
@article{CRMATH_2010__348_3-4_199_0,
     author = {C\'ecile Hardouin and Xavier Guyon},
     title = {Exact marginals and normalizing constant for {Gibbs} distributions},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {199--201},
     publisher = {Elsevier},
     volume = {348},
     number = {3-4},
     year = {2010},
     doi = {10.1016/j.crma.2009.12.002},
     language = {en},
}
TY  - JOUR
AU  - Cécile Hardouin
AU  - Xavier Guyon
TI  - Exact marginals and normalizing constant for Gibbs distributions
JO  - Comptes Rendus. Mathématique
PY  - 2010
SP  - 199
EP  - 201
VL  - 348
IS  - 3-4
PB  - Elsevier
DO  - 10.1016/j.crma.2009.12.002
LA  - en
ID  - CRMATH_2010__348_3-4_199_0
ER  - 
%0 Journal Article
%A Cécile Hardouin
%A Xavier Guyon
%T Exact marginals and normalizing constant for Gibbs distributions
%J Comptes Rendus. Mathématique
%D 2010
%P 199-201
%V 348
%N 3-4
%I Elsevier
%R 10.1016/j.crma.2009.12.002
%G en
%F CRMATH_2010__348_3-4_199_0
Cécile Hardouin; Xavier Guyon. Exact marginals and normalizing constant for Gibbs distributions. Comptes Rendus. Mathématique, Volume 348 (2010) no. 3-4, pp. 199-201. doi : 10.1016/j.crma.2009.12.002. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2009.12.002/

[1] F. Bartolucci; J. Besag A recursive algorithm for Markov random fields, Biometrika, Volume 89 (2002) no. 3, pp. 724-730

[2] J. Besag Spatial interactions and the statistical analysis of lattice systems, J. R. Stat. Soc. B, Volume 148 (1974), pp. 1-36

[3] X. Guyon Random Fields on a Network: Modeling, Statistics, and Applications, Springer-Verlag, New York, 1995

[4] R. Kindermann; J.L. Snell Markov Random Fields and their Applications, Contemp. Maths., AMS, 1980

[5] M. Khaled, A multivariate generalization of a Markov switching model, Working paper, C.E.S. Université Paris 1, 2008, http://mkhaled.chez-alice.fr/khaled.html

[6] M. Khaled, Estimation bayésienne de modèles espace-état non linéaires, Ph.D. thesis, Université Paris 1, 2008, http://mkhaled.chez-alice.fr/khaled.html

[7] J. Moeller; A.N. Pettitt; R. Reeves; K.K. Berthelsen An efficient Markov chain Monte Carlo method for distributions with intractable normalizing constants, Biometrika, Volume 93 (2006) no. 2, pp. 451-458

[8] A.N. Pettitt; N. Friel; R. Reeves Efficient calculation of the normalizing constant of the autologistic and related models on the cylinder and lattice, J. R. Stat. Soc. B, Volume 65 (2003) no. 1, pp. 235-246

[9] R. Reeves; A.N. Pettitt Efficient recursions for general factorisable models, Biometrika, Volume 91 (2004) no. 3, pp. 751-757

Cited by Sources:

Comments - Policy