Equi-energy sampler with applications in statistical inference and statistical mechanics

Annals of Statistics

Volumn 34, Issue 4, 2006, Pages 1581-1619

  Kou, S C ^a,c   Zhou, Qing ^a,c   Wong, Wing Hung ^b  

^a HARVARD UNIVERSITY   (United States)

^b STANFORD UNIVERSITY   (United States)

^c UNIVERSITY OF CAMBRIDGE   (United Kingdom)

Author keywords

Density of states; Energy; Estimation; Microcanonical distribution; Motif sampling; Protein folding; Sampling; Temperature

Indexed keywords

EID: 33748779178     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/009053606000000515     Document Type: Review

References (41)

1. BAILEY, T. L. and ELKAN, C. (1994). Fitting a mixture model by expectation maximization to discover motifs in biopolymers. Proc. Second International Conference on Intelligent Systems for Molecular Biology 2 28-36. AAAI Press, Menlo Park, CA.
2. BERG, B. A. and NEUHAUS, T. (1991). Multicanonical algorithms for first order phase-transitions. Phys. Lett. B 267 249-253.
3. BESAG, J. and GREEN, P. J. (1993). Spatial statistics and Bayesian computation. J. Roy. Statist. Soc. Ser. B 55 25-37. MR1210422
4. DILL, K. A. and CHAN, H. S. (1997). From Levinthal to pathways to funnels. Nature Structural Biology 4 10-19.
5. EDWARDS, R. G. and SOKAL, A. D. (1988). Generalization of the Fortuin-Kasteleyn-Swendsen-Wang representation and Monte Carlo algorithm. Phys. Rev. D (3) 38 2009-2012. MR0965465
6. GELFAND, A. E. and SMITH, A. F. M. (1990). Sampling-based approaches to calculating marginal densities. J. Amer. Statist. Assoc. 85 398-409. MR 1141740
7. GEMAN, S. and GEMAN, D. (1984). Stochastic relaxation, Gibbs distributions and the Bayesian restoration of images. IEEE Trans. Pattern Analysis and Machine Intelligence 6721-741.
8. GEYER, C. J. (1991). Markov chain Monte Carlo maximum likelihood. In Computing Science and Statistics: Proc. 23rd Symposium on the Interface (E. M. Keramidas, ed.) 156-163. Interface Foundation, Fairfax Station, VA.
9. GEYER, C. J. (1994). Estimating normalizing constants and reweighting mixtures in Markov chain Monte Carlo. Technical Report 568, School of Statistics, Univ. Minnesota.
10. GEYER, C. J. and THOMPSON, E. (1995). Annealing Markov chain Monte Carlo with applications to ancestral inference. J. Amer. Statist. Assoc. 90 909-920.
11. HASTINGS, W. K. (1970). Monte Carlo sampling methods using Markov chains and their applications. Biometrika 57 97-109.
12. HIGDON, D. M. (1998). Auxiliary variable methods for Markov chain Monte Carlo with applications. J. Amer. Statist. Assoc. 93 585-595.
13. HUKUSHIMA, K. and NEMOTO, K. (1996). Exchange Monte Carlo and application to spin glass simulations. J. Phys. Soc. Japan 65 1604-1608.
14. JENSEN, S. T., LIU, X. S., ZHOU, Q. and LIU, J. S. (2004). Computational discovery of gene regulatory binding motifs: A Bayesian perspective. Statist. Sci. 19 188-204. MR2082154
15. KONG, A., LIU, J. S. and WONG, W. H. (1994). Sequential imputations and Bayesian missing data problems. J. Amer. Statist. Assoc. 89 278-288.
16. KOU, S. C., OH, J. and WONG, W. H. (2006). A study of density of states and ground states in hydrophobic-hydrophilic protein folding models by equi-energy sampling. J. Chemical Physics 124 244903.
17. KOU, S. C., XIE, X. S. and LIU, J. S. (2005). Bayesian analysis of single-molecule experimental data (with discussion). Appl. Statist. 54 469-506. MR2137252
18. LANDAU, D. P. and BINDER, K. (2000). A Guide to Monte Carlo Simulations in Statistical Physics. Cambridge Univ. Press. MR 1781083
19. LAU, K. F. and DILL, K. A. (1989). A lattice statistical mechanics model of the conformational and sequence spaces of proteins. Macromolecules 22 3986-3997.
20. LAWRENCE, C. E., ALTSCHUL, S. F., BOGUSKI, M. S., LIU, J. S., NEUWALD, A. F. and WOOTTON, J. (1993). Detecting subtle sequence signals: A Gibbs sampling strategy for multiple alignment. Science 262 208-214.
21. LAWRENCE, C. E. and REILLY, A. A. (1990). An expectation maximization (EM) algorithm for the identification and characterization of common sites in unaligned biopolymer sequences. Proteins 741-51.
22. Li, K.-H. (1988). Imputation using Markov chains. J. Statist. Comput. Simulation 30 57-79. MR 1005883
23. LIANG, F. and WONG, W. H. (2001). Real-parameter evolutionary Monte Carlo with applications to Bayesian mixture models. J. Amer. Statist. Assoc. 96 653-666. MR1946432
24. LIU, J. S. (1994). The collapsed Gibbs sampler in Bayesian computations with applications to a gene regulation problem. J. Amer. Statist. Assoc. 89 958-966. MR 1294740
25. LIU, J. S., NEUWALD, A. F. and LAWRENCE, C. E. (1995). Bayesian models for multiple local sequence alignment and Gibbs sampling strategies. J. Amer. Statist. Assoc. 90 1156-1170.
26. LIU, X., BRUTLAG, D. L. and LIU, J. S. (2001). BioProspector: Discovering conserved DNA motifs in upstream regulatory regions of co-expressed genes. In Pacific Symp. Biocomputing 6 127-138.
27. MARINARI, E. and PARISI, G. (1992). Simulated tempering: A new Monte Carlo scheme, Europhys. Lett. 19451-458.
28. MENG, X.-L. and WONG, W. H. (1996). Simulating ratios of normalizing constants via a simple identity: A theoretical exploration. Statist. Sinica 6 831-860. MR1422406
29. METROPOLIS, N., ROSENBLUTH, A. W., ROSENBLUTH, M. N., TELLER, A. H. and TELLER, E. (1953). Equations of state calculations by fast computing machines. J. Chemical Physics 21 1087-1091.
30. MIRA, A., MOLLER, J. and ROBERTS, G. (2001). Perfect slice samplers. J. R. Stat. Soc. Ser. B Stat. Methodol. 63 593-606. MR 1858405
31. NEAL, R. M. (2003). Slice sampling (with discussion). Ann. Statist. 31 705-767. MR1994729
32. ROBERTS, G. and ROSENTHAL, J. S. (1999). Convergence of slice sampler Markov chains. J. R. Stat. Soc. Ser. B Stat. Methodol. 61 643-660. MR 1707866
33. ROTH, F. P., HUGHES, J. D., ESTEP, P. W. and CHURCH, G. M. (1998). Finding DNA regulatory motifs within unaligned noncoding sequences clustered by whole-genome mRNA quantitation. Nature Biotechnology 16 939-945.
34. SCHNEIDER, T. D. and STEPHENS, R. M. (1990). Sequence logos: A new way to display consensus sequences. Nucleic Acids Research 18 6097-6100.
35. SELA, M., WHITE, F. H. and ANFINSEN, C. B. (1957). Reductive cleavage of disulfide bridges in ribonuclease. Science 125 691-692.
36. STORMO, G. D. and HARTZELL, G. W. (1989). Identifying protein-binding sites from unaligned DNA fragments. Proc. Natl. Acad. Sci. USA 86 1183-1187.
37. SWENDSEN, R. H. and WANG, J.-S. (1987). Nonuniversal critical dynamics in Monte Carlo simulations. Phys. Rev. Lett. 58 86-88.
38. TANNER, M. A. and WONG, W. H. (1987). The calculation of posterior distributions by data augmentation (with discussion). J. Amer. Statist. Assoc. 82 528-550. MR0898357
39. TIERNEY, L. (1994). Markov chains for exploring posterior distributions (with discussion). Ann. Statist. 22 1701-1762. MR1329166
40. WANG, F. and LANDAU, D. P. (2001). Determining the density of states for classical statistical models: A random walk algorithm to produce a flat histogram. Phys. Rev. E 64 056101.
41. ZHOU, Q. and WONG, W. H. (2004). CisModule: De novo discovery of cis-regulatory modules by hierarchical mixture modeling. Proc. Natl. Acad. Sci. USA 101 12114-12119.