Outperforming the Gibbs sampler empirical estimator for nearest-neighbor random fields

Annals of Statistics

Volumn 24, Issue 4, 1996, Pages 1433-1456

  Greenwood, Priscilla E ^a   McKeague, Ian W ^b   Wefelmeyer, Wolfgang ^c  

^a UNIVERSITY OF BRITISH COLUMBIA   (Canada)

^b FLORIDA STATE UNIVERSITY   (United States)

^c UNIVERSITY OF SIEGEN   (Germany)

Author keywords

Asymptotic relative efficiency; Ising model; Markov chain Monte Carlo; Metropolis Hastings algorithm; Parallel updating; Variance reduction

Indexed keywords

EID: 0030363220     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/aos/1032298276     Document Type: Article

References (39)

1. AMIT, Y. and GRENANDER, U. (1991). Comparing sweep strategies for stochastic relaxation. J. Multivariate Anal. 37 197-222.
2. ATHREYA, K. B., Doss, H. and SETHURAMAN, J. (1996). On the convergence of the Markov chain simulation method. Ann. Statist. 24 69-100.
3. BESAG, J. and GREEN, P. J. (1993). Spatial statistics and Bayesian inference. J. Roy. Statist. Soc. Ser. B 55 25-37.
4. BICKEL, P. J., KLAASSEN, C. A. J., RITOV, Y. and WELLNER, J. A. (1993). Efficient and Adaptive Estimation for Semiparametric Models. Johns Hopkins Univ. Press.
5. BINDER, K., ed. (1992). The Monte Carlo Method in Condensed Matter Physics. Springer, Berlin.
6. BRILLINGER, D. R. (1963). A note on re-use of samples. Ann. Math. Statist. 34 341-343.
7. CHAN, K. S. (1993). Asymptotic behavior of the Gibbs sampler. J. Amer. Statist. Assoc. 88 320-326.
8. CHAN, K. S. and GEYER, C. J. (1994). Comment on "Markov chains for exploring posterior distributions," by L. Tierney. Ann. Statist. 22 1747-1758.
9. FRIGESSI, A., HWANG, C.-R., SHEU, S. J. and DI STEFANO, P. (1993). Convergence rates of the Gibbs sampler, the Metropolis algorithm, and other single-site updating dynamics. J. Roy. Statist. Soc. Ser. B 55 205-220.
10. FRIGESSI, A., HWANG, C.-R. and YOUNES, L. (1992). Optimal spectral structure of reversible stochastic matrices, Monte Carlo methods and the simulation of Markov random fields. Ann. Appl. Probab. 2 610-628.
11. GELFAND, A. E., HILLS, S. E., RACINE-POON, A. and SMITH, A. F. M. (1990). Illustration of Bayesian inference in normal data models using Gibbs sampling. J. Amer. Statist. Assoc. 85 972-985.
12. GELFAND, A. E. and SMITH, A. F. M. (1990). Sampling-based approaches to calculating marginal densities. J. Amer. Statist. Assoc. 85 398-409.
13. GEMAN, S. and GEMAN, D. (1984). Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images. IEEE Trans. Pattern Anal. Mach. Intell. 6 721-741.
14. GEORGE, E. I. and ROBERT, C. P. (1992). Capture-recapture estimation via Gibbs sampling. Biometrika 79 677-683.
15. GEWEKE, J. (1992). Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments (with discussion). In Bayesian Statistics (J. M. Bernardo, J. O. Berger, A. P. Dawid and A. F. M. Smith, eds.) 4 169-193. Oxford Univ. Press.
16. GEYER, C. J. (1992). Practical Markov chain Monte Carlo. Statist. Sci. 7 473-483.
17. GRAHAM, J. (1994). Monte Carlo Markov chain likelihood ratio test and Wald test for binary spatial lattice data. Preprint.
18. GREEN, P. J. and HAN, X.-L. (1992). Metropolis methods, Gaussian proposals and antithetic variables. In Stochastic Models, Statistical Methods, and Algorithms in Image Analysis. Lecture Notes in Statist. (P. Barone, A. Frigessi and M. Piccioni, eds.) 74 142-164. Springer, Berlin.
19. GREENWOOD, P. E., MCKEAGUE, I. W. and WEFELMEYER, W. (1995). Information bounds for Gibbs samplers. Unpublished manuscript.
20. GRENANDER, U. (1983). Tutorial in pattern theory. Lecture Notes, Division Appl. Math., Brown Univ.
21. GRENANDER, U. (1993). General Pattern Theory. A Mathematical Study of Regular Structures. Clarendon, Oxford.
22. 2 Euclidean quantum field theory as classical statistical mechanics. Ann. Math. 101 111-259.
23. HEERMANN, D. W. and BURKITT, A. N. (1992). Parallel algorithms for statistical physics problems. In The Monte Carlo Method in Condensed Matter Physics (K. Binder, ed.) 53-74. Springer, Berlin.
24. INGRASSIA, S. (1994). On the rate of convergence of the Metropolis algorithm and Gibbs sampler by geometric bounds. Ann. Appl. Probab. 4 347-389.
25. ISRAEL, R. B. (1979). Convexity in the Theory of Lattice Gases. Princeton Univ. Press.
26. KINDERMANN, R. and SNELL, J. L. (1980). Markov Random Fields and Their Applications. Amer. Math. Soc., Providence.
27. LEVIT, B. YA. (1974). On optimality of some statistical estimates. In Proceedings of the Prague Symposium on Asymptotic Statistics (J. Hájek, ed.) 2 215-238. Charles Univ., Prague.
28. MEYN, S. P. and TWEEDIE, R. L. (1993). Markov Chains and Stochastic Stability. Springer, London.
29. PEARL, J. (1987). Evidential reasoning using stochastic simulation. Artificial Intelligence 32 245-257.
30. PENEV, S. (1991). Efficient estimation of the stationary distribution for exponentially ergodic Markov chains. J. Statist. Plann. Inference 27 105-123.
31. PESKUN, P. H. (1973). Optimum Monte Carlo sampling using Markov chains. Biometrika 60 607-612.
32. SCHERVISH, M. J. and CARLIN, B. P. (1992). On the convergence of successive substitution sampling. J. Comput. Graph. Statist. 1 111-127.
33. 2Euclidean (Quantum) Field Theory. Princeton Univ. Press.
34. SMITH, A. F. M. and ROBERTS, G. O. (1993). Bayesian computation via the Gibbs sampler and related Markov chain Monte Carlo methods. J. Roy. Statist. Soc. Ser. B 55 3-23.
35. SPIEGELHALTER, D. J., DAWID, A. P., LAURITZEN, S. L. and COWELL, R. G. (1993). Bayesian analysis in expert systems. Statist. Sci. 8 219-283.
36. SWENDSEN, R. H. and WANG, J.-S. (1987). Nonuniversal critical dynamics in Monte Carlo simulations. Phys. Rev. Lett. 58 86-88.
37. TANNER, M. A. and WONG, W. H. (1987). The calculation of posterior distributions by data augmentation. J. Amer. Statist. Assoc. 82 528-540.
38. TIERNEY, L. (1994). Markov chains for exploring posterior distributions (with discussion). Ann. Statist. 22 1701-1762.
39. WINKLER, G. (1995). Image Analysis, Random Fields and Dynamic Monte Carlo Methods. Springer, Berlin.