Efficient recursions for general factorisable models

Biometrika

Volumn 91, Issue 3, 2004, Pages 751-757

  Reeves, R ^a   Pettitt, And A N ^a  

^a QUEENSLAND UNIVERSITY OF TECHNOLOGY   (Australia)

Author keywords

Autologistic distribution; Gibbs distribution; Ising model; Markov chain monte carlo; Normalising constant; Partition function

Indexed keywords

EID: 24944590473     PISSN: 00063444     EISSN: None     Source Type: Journal    
DOI: 10.1093/biomet/91.3.751     Document Type: Article

References (22)

1. ARNOLD, B. C., CASTILLO, E. & SARABIA, J. M. (2001). Conditionally specified distributions: An introduction (with Discussion). Statist. Sci. 16, 249-74.
2. BARTOLUCCI, F. & BESAG, J. (2002). A recursive algorithm for Markov random fields. Biometrika 89, 724-30.
3. CASELLA, G. (1996). Statistical inference and Monte Carlo algorithms (with Discussion). Test 5, 249-344.
4. CRESSIE, N. & DAVIDSON, J. (1998). Image analysis with partially ordered Markov models. Comp. Statist. Data Anal. 29, 1-26.
5. FRIEL, N. & PETTITT, A. N. (2004). Likelihood estimation and inference for the autologistic model. J. Comp. Graph. Statist. 13, 232-46.
6. GELMAN, A. & MENG, X.-L. (1998). Simulating normalizing constants: from importance sampling to bridge sampling to path sampling. Statist. Sci. 13, 163-85.
7. GEORGE, A. & LIU, J. (1981). Computer Solution of Large Sparse Positive Definite Systems. Englewood Cliffs, NJ: Prentice-Hall.
8. GEYER, C. J. & THOMPSON, E. A. (1992). Constrained Monte Carlo maximum likelihood for dependent data (with Discussion). J. R. Statist. Soc. B 54, 657-99.
9. GREEN, P. J. & RICHARDSON, S. (2002). Hidden Markov models and disease mapping, J. Am. Statist. Assoc. 97, 1055-70.
10. GU, M. G. & ZHU, H.-T. (2001). Maximum likelihood estimation for spatial models by Markov chain Monte Carlo stochastic approximation. J. R. Statist. Soc. B 63, 339-55.
11. HUANG, F. & OGATA, Y. (1999). Improvements of the maximum pseudo-likelihood estimators in various spatial statistical models. J. Comp. Graph. Statist. 8, 510-30.
12. HUFFER, F. W. & WU, H. (1998). Markov chain Monte Carlo for autologistic regression models with application to the distribution of plant species. Biometrics 54, 509-24.
13. JERRUM, M. & SINCLAIR, A. (1993). Polynomial-time approximation algorithms for the Ising model. SIAM J. Comp. 22, 1087-116.
14. KAISER, M. S. & CRESSIE, N. (2000). The construction of multivariate distributions from Markov random fields. J. Mult. Anal. 73, 199-220.
15. MENG, X. (1996). Discussion of 'Statistical inference and Monte Carlo algorithms', by G. Casella. Test 5, 310-8.
16. MOYEED, R. & BADDELEY, A. (1991). Stochastic approximation of the MLE for a spatial point pattern. Scand. J. Statist. 18, 39-50.
17. OGATA, Y. & TANEMURA, M. (1981). Estimation of interaction potentials of spatial point patterns through the maximum likelihood procedure. Ann. Inst. Statist. Math. 33, 315-38.
18. PENTTINEN, A. (1984). Modelling Interactions in Spatial Point Processes: Parameter Estimation by the Maximum Likelihood Method, Jyvaskyla studies in computer science, economics, and statistics, 7. Jyvaskyla, Finland: Jyvaskylan yliopisto.
19. PETTITT, A. N., FRIEL, N. & REEVES, R. (2003). Efficient calculation of the normalising constant of the autologistic and related models on the cylinder and lattice. J. R. Statist. Soc. B 65, 235-46.
20. SCOTT, S. L. (2002). Bayesian methods for hidden Markov models: Recursive computing in the 21st century. J. Am. Statist. Assoc. 97, 337-51.
21. YOUNES, L. (1989). Parametric inference for imperfectly observed Gibbsian fields. Prob. Theory Rel. Fields 82, 625-45.
22. ZUCCHINI, W. & GUTTORP, P. (1991). A hidden Markov model for space time precipitation. Water Resour. Res. 27, 1917-23.