Markov chain Markov field dynamics: Models and statistics

Statistics

Volumn 35, Issue 4, 2001, Pages 593-627

  Guyon, X ^a   Hardouin, C ^a  

^a University Paris I Sorbonne Panthéon   (France)

Author keywords

Auto model; Lyapunov stability criterion; Markov Chain dynamics; Markov field; Martingale CLT theorem; Model diagnostic

Indexed keywords

EID: 0345980094     PISSN: 02331888     EISSN: None     Source Type: Journal    
DOI: 10.1080/02331880108802756     Document Type: Article

References (35)

1. Amemiya, T. (1985) Advanced Econometrics, Blackwell.
2. Arnold, B. C. and Press, J. (1989) Compatible conditional distributions. JASA, 84(405), 152-156.
3. Arnold, B. C. and Strauss, D. (1988) Bivariate distribution with exponential conditionals. JASA, 83(402), 522-527.
4. Arnold, B. C., Castillo, E. and Sarabia, J. M. (1991) Conditionally specified distributions. L.N.S., 74, Springer.
5. Bayomog, S. (1994) Modélisation et analyse des données spatio-temporelles. Ph. D. Thesis, Univ. d'Orsay, France.
6. Bayomog, S., Guyon, X., Hardouin, C. et Yao, J. F. (1996) Test de différence de contraste et somme pondérée de khi-deux. Can. J. Stat., 24(1), 115-130.
7. Bennett, R. J. and Haining, H. (1985) Spatial structure and spatial interaction: modelling approaches to the statistical anaysis of geographical data. JRSS, 148, 1-36.
8. Besag, J. (1974) Spatial interaction an the statistical analysis of lattice systems. JRSS B, 36, 192-236.
9. Besag, J. (1974) On spatial temporal models and Markov fields. 7th Prague Conference and of European Meeting of Statisticians, pp. 47-55.
10. Besag, J. (1977) Efficiency of pseudo likelihood estimation for simple Gaussian fields. Biometrika, 64, 616-618.
11. Chadoeuf, J., Nandris, D., Geiger, J. P., Nicole, M. and Piarrat, J. C. (1992) Modélisation spatio temporelle d'une épidémie par un processus de Gibbs: estimation et tests. Biometrics, 48, 1165-1175.
12. Dacunha-Castelle, D. and Duflo, M. (1986) Probability and Statistics, Vol. 2. Springer, Verlag.
13. Duflo, M. (1997) Random Iterative Models. Springer.
14. Durrett, R. (1995) Ten Lectures on Particles Systems, Saint-Flour 1993. L.N.M. 1608, pp. 97-201, Springer.
15. Garber, D. D. (1981) Computational models for texture analysis and texture synthesis. Ph. D. Thesis, Univ. South California.
16. Geyer, C. (1999) Likelihood inference for spatial point processes, In: Stochastic Geometry, Likelihood and Computation (Chapter 3). Barndorff-Nielsen, Kendall and Van Lieshout (Eds.), Chapman and Hall.
17. Geyer, C. J. and Thompson, E. A. (1992) Constrained Monte Carlo maximum likelihood for dependent data (with discussion). JRSS, B, 54, 657-699.
18. Guyon, X. (1995) Random Fields on a Network: Modeling, Statistics and Applications. Springer.
19. Guyon, X. and Hardouin, C. (1992) The chi2 difference of coding test for testing Markov Random Field hypothesis. L.N.S. 74, Springer, pp. 165-176.
20. Guyon, X. and Künsch, H. R. (1992) Asymptotic comparison of estimators in the Ising model. L.N.S. 74, Springer, pp. 177-198.
21. Hall, P. and Heyde, C. C. (1980) Martingale Limit Theory and its Applications. Acad. Press.
22. Jensen, J. L. and Künsch, H. R. (1994) On asymptotic normality of pseudo-likelihood estimate for pairwise interaction processes. Ann. Inst. Statist. Math., 46, 475-486.
23. Keiding, N. (1975) Maximum likelihood estimation in the Birth and death process. Ann. of Stats., 3, 363-372.
24. Koslov, O. and Vasilyev, N. (1980) Reversible Markov chain with local interaction, In: Multicomponent Random Systems. Dobrushin and Sinai (Eids.), Dekker.
25. Künsch, H. R. (1984) Time reversal and stationary Gibbs measures. Stoch. Proc. and Applications, 17, 159-166.
26. Pfeifer, P. E. and Deutsch, S. J. (1980) Identification and interpretation of first order for Space-time ARMA models. Technometrics, 22, 397-408.
27. Pfeifer, P. E. and Deutsch, S. J. (1980) A three stage iterative procedure for space time modelling. Technometrics, 22, 35-47.
28. Preston, C. (1974) Gibbs States on Countable Set. Cambridge tracts in math 68.
29. Prum, B. (1986) Processus sur un reseau et mesure de Gibbs. Applications. Masson.
30. Ripley, B. (1981) Spatial Statistics. Wiley.
31. Tang van Tham (1991) Rainfall greenhouse effect in the delta of Mekong. Ph. D. Thesis, Univ. of Cantho., Vietnam.
32. Tong, H. (1990) Non Linear Time Series. A Dynamical System Approach. Clarendon Press, Oxford.
33. Younes, L. (1988) Estimation and Annealing for Gibssian fields. Ann. I.H.P. 2, pp. 269-294.
34. Zucchini, W. and Guttorp, P. (1991) A hidden Markov model for space time precipitation. Water Resour. Res., 27, 1917-1923.
35. MacDonald, I. and Zucchini, W. (1997) Hidden Markov and other models for discrete valued time scries. Monographs on Statistic and Applied Probability. Chapman and Hall.