Consistent estimation of the basic neighborhood of markov random fields

Annals of Statistics

Volumn 34, Issue 1, 2006, Pages 123-145

  Csiszár, Imre ^a   Talata, Zsolt ^a  

^a INSTITUTE OF EXPERIMENTAL MEDICINE   (Hungary)

Author keywords

Gibbs measure; Information criterion; Markov random field; Model selection; Pseudo likelihood; Typicality

Indexed keywords

EID: 33744781810     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/009053605000000912     Document Type: Article

References (24)

1. AKAIKE, H. (1972). Information theory and an extension of the maximum likelihood principle. In Proc. Second International Symposium on Information Theory, Supplement to Problems of Control and Information Theory (B. N. Petrov and F. Csáki, eds.) 267-281. Akadémiai Kiadó, Budapest. MR0483125
2. AZENCOTT, R. (1987). Image analysis and Markov fields. In Proc. First International Conference on Industrial and Applied Mathematics, Paris (J. McKenna and R. Temen, eds.) 53-61. SIAM, Philadelphia. MR0976851
3. BESAG, J. (1974). Spatial interaction and the statistical analysis of lattice systems (with discussion). J. Roy. Statist. Soc. Ser. B 36 192-236. MR0373208
4. BESAG, J. (1975). Statistical analysis of non-lattice data. The Statistician 24 179-195.
5. BÜHLMANN, P. and WYNER, A. J. (1999). Variable length Markov chains. Ann. Statist. 27 480-513. MR1714720
6. COMETS, F. (1992). On consistency of a class of estimators for exponential families of Markov random fields on the lattice. Ann. Statist. 20 455-468. MR1150354
7. CSISZÁR, I. (2002). Large-scale typicality of Markov sample paths and consistency of MDL order estimators. IEEE Trans. Inform. Theory 48 1616-1628. MR1909476
8. CSISZÁR, I. and SHIELDS, P. C. (2000). The consistency of the BIC Markov order estimator. Ann. Statist. 28 1601-1619. MR1835033
9. CSISZÁR, I. and TALATA, Zs. (2006). Context tree estimation for not necessarily finite memory processes, via BIC and MDL. IEEE Trans. Inform. Theory 52 1007-1016.
10. DOBRUSHIN, R. L. (1968). The description of a random field by means of conditional probabilities and conditions for its regularity. Theory Probab. Appl. 13 197-224. MR0231434
11. FINESSO, L. (1992). Estimation of the order of a finite Markov chain. In Recent Advances in Mathematical Theory of Systems, Control, Networks and Signal Processing 1 (H. Kimura and S. Kodama, eds.) 643-645. Mita, Tokyo. MR1197985
12. GEMAN, S. and GRAFFIGNE, C. (1987). Markov random field image models and their applications to computer vision. In Proc. International Congress of Mathematicians 2 (A. M. Gleason, ed.) 1496-1517. Amer. Math. Soc., Providence, RI. MR0934354
13. GEORGII, H. O. (1988). Gibbs Measures and Phase Transitions. de Gruyter, Berlin. MR0956646
14. GIDAS, B. (1988). Consistency of maximum likelihood and pseudolikelihood estimators for Gibbs distributions. In Stochastic Differential Systems, Stochastic Control Theory and Applications (W. Fleming and P.-L. Lions, eds.) 129-145. Springer, New York. MR0934721
15. GIDAS, B. (1993). Parameter estimation for Gibbs distributions from fully observed data. In Markov Random Fields: Theory and Application (R. Chellappa and A. Jain, eds.) 471-498. Academic Press, Boston. MR1214376
16. HANNAN, E. J. and QUINN, B. G. (1979). The determination of the order of an autoregression. J. Roy. Statist. Soc. Ser. B 41 190-195. MR0547244
17. HAUGHTON, D. (1988). On the choice of a model to fit data from an exponential family. Ann. Statist. 16 342-355. MR0924875
18. JI, C. and SEYMOUR, L. (1996). A consistent model selection procedure for Markov random fields based on penalized pseudolikelihood. Ann. Appl. Probab. 6 423-443. MR1398052
19. PICKARD, D. K. (1987). Inference for discrete Markov fields: The simplest non-trivial case. J. Amer. Statist. Assoc. 82 90-96. MR0883337
20. RÉNYI, A. (1970). Probability Theory. North-Holland, Amsterdam. MR0315747
21. SCHWARZ, G. (1978), Estimating the dimension of a model. Ann. Statist. 6 461-464. MR0468014
22. WEINBERGER, M. J., RISSANEN, J. and FEDER, M. (1995). A universal finite memory source. IEEE Trans. Inform. Theory 41 643-652.
23. WILLEMS, F. M. J., SHTARKOV, Y. M. and TJALKENS, T. J. (1993). The context-tree weighting method: Basic properties. Technical report, Dept. Electrical Engineering, Eindhoven Univ.
24. WILLEMS, F. M. J., SHTARKOV, Y. M. and TJALKENS, T. J. (2000). Context-tree maximizing. In Proc. 2000 Conf. Information Sciences and Systems TP6-7-TP6-12. Princeton, NJ.