A theory for dynamic weighting in monte carlo computation

Journal of the American Statistical Association

Volumn 96, Issue 454, 2001, Pages 561-573

  Liu, Jun S ^a   Liang, Faming ^b   Wong, Wing Hung ^c  

^a HARVARD UNIVERSITY   (United States)

^b NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

^c HARVARD UNIVERSITY   (United States)

Author keywords

Gibbs sampling; Importance sampling; Ising model; Metropolis algorithm; Neural network; Renewal theory; Simulated annealing; Simulated tempering

Indexed keywords

EID: 1542783745     PISSN: 01621459     EISSN: 1537274X     Source Type: Journal    
DOI: 10.1198/016214501753168253     Document Type: Article

References (38)

1. Ackley, D. H., Hinton, G. R., and Sejnowski, T. J. (1985), “A Learning Algorithm for Boltzmann Machines,” Cognitive Science, 9, 147–169.
2. Asmussen, S. (1987), Applied Probability and Queues, New York: Wiley.
3. Berg, B. A., and Neuhaus, T. (1991), “Multicanonical Algorithms for First-Order Phase Transitions,” Physics Letters, Ser. B, 267, 249.
4. Chung, K. L. (1974), A Course in Probability Theory, New York: Academic Press.
5. Dembo, A., and Zeitouni, O. (1993), Large Deviations Techniques, Boston: Jones and Bartlett.
6. Frenkel, D., and Smit, B. (1996), Understanding Molecular Simulation: From Algorithms to Applications, New York: Academic Press.
7. Gelfand, A. E., and Smith, A. F. M. (1990), “Sampling-Based Approaches to Calculating Marginal Densities,” Journal of the American Statistical Association, 85, 398–409.
8. Geman, S., and Geman, D. (1984), “Stochastic Relaxation, Gibbs Distributions and the Bayesian Restoration of Images,” IEEE Transaction on Pattern Analysis and Machine Intelligence, 6, 721–741.
9. Geyer, C. J., and Thompson, E. A. (1995), “Annealing Markov Chain Monte Carlo With Applications to Ancestral Inference,” Journal of the American Statistical Association, 90, 909–920.
10. Goodman, J., and Sokal, A. D. (1989), “Multigrid Monte Carlo Method. Conceptual Foundations,” Physical Review D, 40, 2035–2071.
11. Green, P. J. (1995), “Reversible Jump Markov Chain Monte Carlo Computation and Bayesian Model Determination,” Biometrika, 82, 711–732.
12. Hastings, W. K. (1970), “Monte Carlo Sampling Methods Using Markov Chains and Their Applications,” Biometrika, 57, 97–109.
13. Hopfield, J. J. (1982), “Neural Networks and Physical Systems With Emergent Collective Computational Abilities.” Proceedings of the National Academy of Sciences, 79, 2554–2558.
14. Kesten, H. (1974) “Renewal Theory for Markov Chains,” The Annals of Probability, 2, 355–387.
15. Kirkpatrick, S., Gelatt, C. D. Jr., and Vecchi, M. P. (1983), “Optimization by Simulated Annealing,” Science, 220, 671–680.
16. Kohonen, T. (1989), Self-Organizing and Associative Memory, Berlin: Springer-Verlag.
17. Lang, K. J., and Witbrock, M. J. (1989), “Learning to Tell Two Spirals Apart,” in Proceedings of 1988 Connectionist Models Summer School, pp. 52–59.
18. Lawrence C. E., Altschul, S. F., Boguski, M. S., Liu, J. S., Neuwald, A. F., and Wootton, J. C. (1993), “Detecting Subtle Sequence Signals: A Gibbs Sampling Strategy for Multiple Alignment,” Science, 262, 208–214.
19. Leach, A. R. (1996), Molecular Modeling: Principles and Applications, Singapore: Addison Wesley Longman.
20. Lezaud, P. (1998), “Chernoff-Type Bound for Finite Markov Chains,” Annals of Applied Probability, 8, 849–867.
21. Liang, F. (1997), “Weighted Markov Chain Monte Carlo and Optimization,” unpublished doctorial thesis, The Chinese University of Hong Kong.
22. Liang, F., and Wong, W. H. (1999), “Dynamic Weighting in Simulations of Spin Systems,” Physics Letters, Ser. A, 252, 257–262.
23. Liu, J. S., Neuwald, A. F., and Lawrence, C. E. (1999), “Markovian Structures in Biological Sequence Alignments,” Journal of the American Statistical Association, 94, 1–15.
24. Liu, J. S., and Sabattti, C. (1998), “Simulated Sintering: Markov Chain Monte Carlo with Spaces of Varying Dimension,” in Bayesian Statistics, 6, 389–413, eds. J. M. Bernardo, J. O. Berger, A. P. Dawid, and A. F. M. Smith, New York, Oxford University Press.
25. Liu, J. S., Wong, W. H., and Kong, A. (1994), “Covariance Structure of the Gibbs Sampler With Applications to the Comparisons of Estimators and Augmentation Schemes,” Biometrika, 81, 27–40.
26. Liu, J. S., Liang, F., and Wong, W. H. (2000), “The Multiple-try Method and Local Optimization in Metropolis Sampling,” Journal of the American Statistical Association, 95, 121–134.
27. Marinari, E., and Parisi, G. (1992), “Simulated Tempering: A New Monte Carlo Scheme,” Europhysics Letters, 19, 451.
28. Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N., Teller, A. H., and Teller, E. (1953), “Equations of State Calculations by Fast Computing Machines,” Journal of Chemical Physics, 21, 1087-1091.
29. Neal, R. M. (1996), Bayesian Learning for Neural Networks, New York: Springer.
30. Nummelin, E. (1984), General Irreducible Markov Chains and Non-Negative Operators, New York: Cambridge University Press.
31. Onsager, L. (1949), “Statistical Hydrodynamics,” Nuovo Cimento (Suppl.), 6, 261.
32. Ripley, D. (1996), Pattern Recognition and Neural Networks, Cambridge, U.K.: Cambridge University Press.
33. Rumelhart, D. E., Hinton, G. E., and Williams, R. J. (1986), “Learning Representations by Back-Propagating Errors,” Nature, 323, 533–536.
34. Rumelhart, D. E., and McClelland, J. (1986), Parallel Distributed Processing: Exploitations in the Micro-Structure of Cognition, Vols. 1 and 2, Cambridge, MA: MIT Press.
35. Swendsen, R. H., and Wang, J. S. (1987), “Nonuniversal Critical Dynamics in Monte Carlo Simulations,” Physics Review Letters, 58, 86.
36. Tanner, M. A., and Wong, W. H. (1987), “The Calculation of Posterior Distribution by Data Augmentation” (with discussion), Journal of the American Statistical Association, 82, 528–550.
37. Wong, W. H., and Liang, F. (1997), “Dynamic Weighting in Monte Carlo and Optimization,” Proceedings of the National Academy of Science, 94, 14220–14224.
38. Yang, C. N. (1952), “The Spontaneous Magnetization of a Two-Dimensional Ising Model,” Physics Review, 85, 808.