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.
Accepted:
Published online:
Cécile Hardouin 1; Xavier Guyon 1
@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}, }
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] A recursive algorithm for Markov random fields, Biometrika, Volume 89 (2002) no. 3, pp. 724-730
[2] Spatial interactions and the statistical analysis of lattice systems, J. R. Stat. Soc. B, Volume 148 (1974), pp. 1-36
[3] Random Fields on a Network: Modeling, Statistics, and Applications, Springer-Verlag, New York, 1995
[4] 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] An efficient Markov chain Monte Carlo method for distributions with intractable normalizing constants, Biometrika, Volume 93 (2006) no. 2, pp. 451-458
[8] 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] Efficient recursions for general factorisable models, Biometrika, Volume 91 (2004) no. 3, pp. 751-757
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