A consistent model selection procedure for Markov random fields based on penalized pseudolikelihood

Annals of Applied Probability

Volumn 6, Issue 2, 1996, Pages 423-443

  Ji, Chuanshu ^a   Seymour, Lynne ^b  

^a University of North Carolina at Chapel Hill   (United States)

^b UNIVERSITY OF GEORGIA   (United States)

Author keywords

Gibbs random fields; Image analysis; Markov random fields; Model selection; Pseudolikelihood; Texture synthesis

Indexed keywords

EID: 0030509462     PISSN: 10505164     EISSN: None     Source Type: Journal    
DOI: 10.1214/aoap/1034968138     Document Type: Article

References (28)

1. AKAIKE, H. (1974). A new look at statistical model identification. IEEE Trans. Automat. Control 10 716-723.
2. AKAIKE, H. (1978). A Bayesian analysis of the minimum AIC procedure. Ann. Inst. Statist. Math. 30 9-14.
3. BARNDORFF-NIELSEN, O. (1978). Information and Exponential Families in Statistical Theory. Wiley, New York.
4. BESAG, J. (1974). Spatial interaction and the statistical analysis of lattice systems. J. Roy. Statist. Soc. Ser. B 6 192-236.
5. BROWN, L. D. (1986). Fundamentals of Statistical Exponential Families with Applications in Statistical Decision Theory. IMS, Hayward, CA.
6. COMÉTS, F. (1992). On consistency of a class of estimators for exponential families of Markov random fields on the lattice. Ann. Statist. 20 455-468.
7. CROSS, G. and JAIN, A. (1983). Markov random field texture models. IEEE Transactions on Pattern Analysis and Machine Intelligence 5 25-39.
8. GEMAN, D. (1991). Random Fields and Inverse Problems in Imaging. Lecture Notes in Math. 1427 113-193. Springer, New York.
9. GEMAN, S. and GEMAN, D. (1984). Stochastic relaxation, Gibbs distributions, and Bayesian restoration of images. IEEE Transactions on Pattern Analysis and Machine Intelligence 6 721-741.
10. GEMAN, S. and C. GRAFFIGNE (1986). Markov random field image models and their applications to computer vision. Proceedings of the International Congress of Mathematicians 1496-1517. Berkeley, CA.
11. GEORGII, H. O. (1988). Gibbs Measures and Phase Transitions. de Gruyter, Berlin.
12. GEYER, C. J. and THOMPSON, E. A. (1992). Constrained Monte Carlo maximum likelihood for dependent data. J. Roy. Statist. Soc. Ser. B 54 657-699.
13. GIDAS, B. (1988). Consistency of maximum likelihood and maximum pseudo-likelihood estimators for Gibbs distributions. In Stochastic Differential Systems, Stochastic Control Theory and Applications (W. Fleming and P.-L. Lyons, eds.) 129-146. Springer, New York.
14. GIDAS, B. (1993). Parameter estimation for Gibbs distributions from fully observed data. In Markov Random Fields: Theory and Applications (R. Chellappa and A. Jain, eds.) 471-498. Academic Press, New York.
15. HASSNER, M. and SKLANSKY, J. (1980). The use of Markov random fields as models of texture. Computer Graphics and Image Processing 12 357-370.
16. JI, C. (1990). Sieve estimators for pair-interaction potentials and local characteristics in Gibbs random fields. Technical Report 2037, Dept. Statistics, Univ. North Carolina.
17. KARR, A. (1991). Statistical models and methods in image analysis: a survey. In Inference for Stochastic Processes (I. V. Basawa and N. U. Prabhu, eds.). Dekker, New York.
18. KASHYAP, R. and CHELLAPPA, R. (1983). Estimation and choice of neighbors in spatial interaction models of images. IEEE Trans. Inform. Theory 29 60-72.
19. KÜNSCH, H., GEMAN, S. and KEHAGIAS, A. (1995). Hidden Markov random fields. Ann. Appl. Probab. 5 577-602.
20. RIPLEY, B. D. (1981). Spatial Statistics. Wiley, New York.
21. RISSANEN, J. (1984). Stochastic complexity. J. Roy. Statist. Soc. Ser. B 49 223-239.
22. ROSENFELD, A. (1993). Image modeling during the 1980's: a brief overview. In Markov Random Fields: Theory and Applications (R. Chellappa and A. Jain, eds.). Academic Press, New York.
23. RUBIN, H. and SETHURAMAN, J. (1965). Probabilities of moderate deviations. Sankhyā Ser. A 27 325-346.
24. SCHWARZ, G. (1978). Estimating the dimension of a model. Ann. Statist. 6 461-464.
25. SEYMOUR, L. (1993). Parameter estimation and model selection in image analysis using Gibbs-Markov random fields. Ph.D. dissertation, Dept. Statistics, Univ. North Carolina.
26. SEYMOUR, L. and JI, C. (1996). Approximate Bayes model selection criteria for Markov random fields. J. Statist. Plann. Inference 51 75-97.
27. SMITH, K. and MILLER, M. (1990). A Bayesian approach incorporating Rissanen complexity for learning Markov random field texture models. Proceedings of the 15th International Conference on Acoustics, Speech, and Signal Processing 4 2317-2320.
28. WOODROOFE, M. (1982). On model selection and the arcsine laws. Ann. Statist. 10 1182-1194.