Stochastic approximation in Monte Carlo computation

Journal of the American Statistical Association

Volumn 102, Issue 477, 2007, Pages 305-320

  Liang, Faming ^a   Liu, Chuanhai Liu ^b   Carroll, Raymond J ^a  

^a TEXAS A AND M UNIVERSITY   (United States)

^b PURDUE UNIVERSITY   (United States)

Author keywords

Importance sampling; Markov chain Monte Carlo; Model selection; Spatial autologistic model; Stochastic approximation; Wang landau algorithm

Indexed keywords

EID: 33947215681     PISSN: 01621459     EISSN: None     Source Type: Journal    
DOI: 10.1198/016214506000001202     Document Type: Article

References (61)

1. Andrieu, C., Moulines, É., and Priouret, P. (2005), "Stability of Stochastic Approximation Under Verifiable Conditions," SIAM Journal of Control and Optimization, 44, 283-312.
2. Augustin, N., Mugglestone, M., and Buckland, S. (1996), "An Autologistic Model for Spatial Distribution of Wildlife," Journal of Applied Ecology, 33, 339-347.
3. Besag, J. E. (1974), "Spatial Interaction and the Statistical Analysis of Lattice Systems" (with discussion), Journal of the Royal Statistical Society, Ser. B, 36, 192-236.
4. _ (1975), "Statistical Analysis of Non-Lattice Data," The Statistician, 24, 179-195.
5. Benveniste, A., Métivier, M., and Priouret, P. (1990), Adaptive Algorithms and Stochastic Approximations, New York: Springer-Verlag.
6. Berg, B. A., and Neuhaus, T. (1991), "Multicanonical Algorithms for 1st-Order Phase-Transitions," Physics Letters B, 267, 249-253.
7. Cappé, O., Guillin, A., Marin, J. M., and Robert, C. P. (2004), "Population Monte Carlo," Journal of Computational and Graphical Statistics, 13, 907-929.
8. Delyon, B., Lavielle, M., and Moulines, E. (1999), "Convergence of a Stochastic Approximation Version of the EM Algorithm," The Annals of Statistics, 27, 94-128.
9. Diggle, P. J., and Gratton, R. J. (1984), "Monte Carlo Methods of Inference for Implicit Statistical Models" (with discussion), Journal of the Royal Statistical Society, Ser, B, 46, 193-227.
10. Efron, B., and Tibshirani, R. J. (1993), An Introduction to the Bootstrap, London: Chapman & Hall.
11. Gelfand, A. E., and Banerjee, S. (1998), "Computing Marginal Posterior Modes Using Stochastic Approximation," technical report, University of Connecticut, Dept. of Statistics.
12. Gelman, A., and Rubin, D. B. (1992), "Inference From Iterative Simulation Using Multiple Sequences" (with discussion), Statistical Science, 7, 457-472.
13. Geman, S., and Geman, D. (1984), "Stochastic Relaxation, Gibbs Distributions and the Bayesian Restoration of Images," IEEE Transactions on Pattern Analysis and Machine Intelligence, 6, 721-741.
14. Geyer, C. J. (1991), "Markov Chain Monte Carlo Maximum Likelihood," in Computing Science and Statistics: Proceedings of the 23rd Symposium on the Interface, ed. E. M. Keramigas, Fairfax, VA: Interface Foundation, pp. 156-163.
15. _ (1992). "Practical Monte Carlo Markov Chain" (with discussion). Statistical Science, 7, 413-511.
16. _ (1994), "On the Convergence of Monte Carlo Maximum Likelihood Calculations." Journal of the Royal Statistical Society, Set. B. 56, 261-274.
17. _ (1996). "Estimation and Optimization of Functions." in Markov Chain Monte Carlo in Practice, eds. W. R. Gilks. S. Richardson, and D. J. Spiegelhalter. London: Chapman & Hall, pp. 241-258.
18. Geyer, C. J., and Thompson, E. A. (1992), "Constrained Monte Carlo Maximum Likelihood for Dependent Data." Journal of the Royal Statistical Society. Ser. B. 54. 657-699.
19. _ (1995), "Annealing Markov Chain Monte Carlo With Applications to Ancestral Inference." Journal of the American Statistical Association, 90. 909-920.
20. Gilks, W. R., Roberts, R. O., and Sahu. S. K. (1998), "Adaptive Markov Chain Monte Carlo Through Regeneration," Journal of the American Statistical Association, 93, 1045-1054.
21. Green, P. J. (1995), "Reversible-Jump Markov Chain Monte Carlo Computation and Bayesian Model Determination." Biometrika, 82. 711-732.
22. Green, P. J., and Richardson, S. (2002), "Hidden Markov Models and Disease Mapping," Journal of the American Statistical Association, 97, 1055-1070.
23. Gu, M. G., and Kong, F. H. (1998). "A Stochastic Approximation Algorithm With Markov Chain Monte Carlo Method for Incomplete Data Estimation Problems." Proceedings of the National Academy of Sciences USA. 95. 7270-7274.
24. Gu. M. G., and Zhu, H. T. (2001). "Maximum Likelihood Estimation for Spatial Models by Markov Chain Monte Carlo Stochastic Approximation." Journal of the Royal Statistical Society, Ser. B, 63, 339-355.
25. Hastings, W. K. (1970). "Monte Carlo Sampling Methods Using Markov Chains and Their Applications," Biometrika, 57, 97-109.
26. Hesselbo, B., and Stinchcombe, R. B. (1995). "Monte Carlo Simulation and Global Optimization Without Parameters," Physical Review Letters. 74. 2151-2155.
27. Hesterberg, T. (1995), "Weighted Average Importance Sampling and Defensive Mixture Distributions," Technometrics, 37, 185-194.
28. Honeycutt, J. D., and Thirumalai, D. (1990), "Metastability of the Folded States of Globular Proteins," Proceedings of the National Academy of Sciences USA. 87, 3526-3529.
29. Hukushima, K., and Nemoto, K. (1996), "Exchange Monte Carlo Method and Application to Spin Glass Simulations," Journal of the Physics Society of Japan, 65, 1604-1608.
30. Jobson, J. D. (1992), Applied Multivariate Data Analysis. Vol. II: Categorical and Multivariate Methods, New York: Springer-Verlag.
31. Lai, T. L. (2003), "Stochastic Approximation." The Annals of Statistics. 31. 391-406.
32. Liang, F. (2002), "Dynamically Weighted Importance Sampling in Monte Carlo Computation," Journal of the American Statistical Association. 97, 807-821.
33. _ (2003), "Use of Sequential Structure in Simulation From HighDimensional Systems." Physical Review E, 67, 56101-56107.
34. _ (2004). "Annealing Contour Monte Carlo for Structure Optimization in an Off-Lattice Protein Model." Journal of Chemical Physics, 120. 6756-6763.
35. _ (2005), "Generalized Wang-Landau Algorithm for Monte Carlo Computation," Journal of the American Statistical Association, 100, 1311-1327.
36. Liang, F., and Wong, W. H. (2001). "Real Parameter Evolutionary Monte Carlo With Applications in Bayesian Mixture Models," Journal of the American Statistical Association, 96, 653-666.
37. Liu, J. S. (2001), Monte Carlo Strate/fies in Scientific Computing. New York: Springer-Verlag.
38. Liu, J. S., Liang. F., and Wong, W. H. (2001), "A Theory for Dynamic Weighting in Monte Carlo." Journal of the American Statistical Association. 96. 561-573.
39. Marinari. E., and Parisi. G. (1992), "Simulated Tempering: A New Monte Carlo Scheme," Europhysics Letters, 19, 451-458.
40. Mengersen, K. L., and Tweedie, R. L. (1996), "Rates of Convergence of the Hastings and Metropolis Algorithms." The Annals of Statistics, 24, 101-121.
41. Metropolis. N., Rosenbluth, A. W., Rosenbluth, M. N., Teller. A. H., and Teller. E. (1953), "Equation of State Calculations by Fast Computing Machines," Journal of Chemical Physics. 21, 1087-1091.
42. Moyeed, R. A., and Baddeley, A. J. (1991), "Stochastic Approximation of the MLE for a Spatial Point Pattern." Scandinavian Journal of Statistics. 18. 39-50.
43. Neal. R. M. (2003). "Slice Sampling" (with discussion), The Annals of Statistics, 31, 105-761.
44. Nevel'son, M. B., and Has'minskii. R. Z. (1973). Stochastic Approximation and Recursive Estimation. Providence. RI: American Mathematical Society.
45. Preisler, H. K. (1993). "Modeling Spatial Patterns of Trees Attacked by Bark Beetles." Applied Statistics, 42, 501-514.
46. Robbins, H., and Monro, S. (1951), "A Stochastic Approximation Method." The Annals of Mathematical Statistics. 22, 400-407.
47. Robert. C. P., and Casella. G. (2004), Monte Carlo Statistical Methods (2nd ed.). New York: Springer-Verlag.
48. Roberts. G. O., and Rosenthal. J. S. (2004). "General State-Space Markov Chains and MCMC Algorithms," Probability Surveys, 1. 20-71.
49. Roberts, G. O., and Tweedie, R. L, (1996), "Geometric Convergence and Central Limit Theorems for Multidimensional Hastings and Metropolis Algorithms." Biometrika, 83, 95-110.
50. Rosenthal, J. S, (1995), "Minorization Conditions and Convergence Rate for Markov Chain Monte Carlo," Journal of the American Statistical Association. 90, 558-566.
51. Sherman. M., Apanasovich, T. V. and Carroll, R. J. (2006). "On Estimation in Binary Autologistic Spatial Models," Journal of Statistical Computation and Simulation, 76, 167-179.
52. Stavropoulos, P., and Titterington, D. M. (2001), "Improved Particle Filters and Smoothing," in Sequential MCMC in Practice, eds. A. Doucet, N. deFreitas. and N. Gordon. New York: Springer-Verlag, pp. 295-318.
53. Swendsen. R. H., and Wang, J. S. (1987), "Nonuniversal Critical Dynamics in Monte Carlo Simulations." Physical Review Letters, 58, 86-88.
54. Tierney, L. (1994), "Markov Chains for Exploring Posterior Distributions" (with discussion), The Annals of Statistics, 22. 1701-1762.
55. Torrie, G. M., and Valleau, J. P. (1977). "Non-Physical Sampling Distributions in Monte Carlo Free Energy Estimation: Umbrella Sampling," Journal of Computational Physics. 23. 187-199.
56. Wang, F., and Landau. D. P. (2001), "Efficient. Multiple-Range Random-Walk Algorithm to Calculate the Density of States." Physical Review Letters. 86, 2050-2053.
57. Warnes, G. R. (2001), "The Normal Kernel Coupler: An Adaptive Markov Chain Monte Carlo Method for Efficiently Sampling From Multi-Modal Distributions." Technical Report 395. University of Washington, Dept. of Statistics.
58. Wong, W. H., and Liang, F. (1997). "Dynamic Weighting in Monte Carlo and Optimization," Proceeding of the National Academy of Sciences USA, 94, 14220-14224.
59. Yan, Q., and de Pablo, J. J. (2003). "Fast Calculation of the Density of States of a Fluid by Monte Carlo Simulations," Physics Review Letters, 90, 035701.
60. Younes, L. (1988), "Estimation and Annealing for Gibbsian Fields," Annales de l'Instut Henri Poincaré, 24, 269-294.
61. _ (1999). "On the Convergence of Markovian Stochastic Algorithms With Rapidly Decreasing Ergodicity Rates." Stochastics and Stochastics Reparts. 65, 177-228.