On population-based simulation for static inference

Statistics and Computing

Volumn 17, Issue 3, 2007, Pages 263-279

  Jasra, Ajay ^a   Stephens, David A ^b   Holmes, Christopher C ^c  

^a IMPERIAL COLLEGE LONDON   (United Kingdom)

^b MCGILL UNIVERSITY   (Canada)

^c UNIVERSITY OF OXFORD   (United Kingdom)

Author keywords

Adaptive methods; Bayesian mixture models; Markov chain Monte Carlo; Sequential Monte Carlo

Indexed keywords

EID: 34547863202     PISSN: 09603174     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11222-007-9028-9     Document Type: Article

References (81)

1. Andrieu, C., Moulines, É.: On the ergodicity properties of some adaptive MCMC algorithms. Ann. Appl. Probab. 16, 1462-1505 (2006)
2. Andrieu, C., Robert, C.P.: Controlled MCMC for optimal sampling. Technical Report, Universitié Paris Dauphine (2001)
3. Andrieu, C., Jasra, A., Doucet, A., Del Moral, P.: Non-linear Markov chain Monte Carlo via self interacting approximations. Technical Report, University of Bristol (2007a)
4. Andrieu, C., Jasra, A., Doucet, A., Del Moral, P.: A note on the convergence of the equi-energy sampler. Technical Report, University of Bristol (2007b). Stoch. Anal. Appl. (to appear)
5. Atchadé, Y.F., Liu, J.S.: The Wang-Landau algorithm for Monte Carlo computation in general state spaces. Technical Report, University of Ottawa (2004)
6. Atchadé, Y.F., Liu, J.S.: Discussion of the 'equi-energy sampler'. Ann. Stat. 34, 1620-1628 (2006)
7. Baker, J.E.: Adaptive selection methods for genetic algorithms. In: Grefenstette, J. (ed.) Proc. Intl. Conf. on Genetic Algorithms and Their Appl., pp. 101-111. Erlbaum, Mahwah (1985)
8. Brockwell, A.E., Del Moral, P., Doucet, A.: Sequentially interacting Markov chain Monte Carlo for Bayesian computation. Technical Report, Carnagie Mellon University (2007)
9. Cappé, O., Guillin, A., Marin, J.M., Robert, C.P.: Population Monte Carlo. J. Comput. Graph. Stat. 13, 907-925 (2004)
10. Chen, Y., Xie, J., Liu, J.S.: Stopping-time resampling for sequential Monte Carlo methods. J. Roy. Stat. Soc. Ser. B 67, 199-217 (2005)
11. Chopin, N.: A sequential particle filter method for static models. Biometrika 89, 539-552 (2002)
12. Chopin, N.: Central limit theorem for sequential Monte Carlo methods and its application to Bayesian inference. Ann. Stat. 32, 2385-2411 (2004)
13. Chopin, N.: Inference and model choice for time-ordered hidden Markov models. J. Roy. Stat. Soc. Ser. B (2007, to appear)
14. Crisan, D., Doucet, A.: Convergence of sequential Monte Carlo methods. Technical Report, University of Cambridge (2000)
15. Del Moral, P.: Feynman-Kac Formulae: Genealogical and Interacting Particle Systems with Applications. Springer, New York (2004)
16. Del Moral, P., Doucet, A.: On a class of genealogical and interacting Metropolis models. In: Azéma, J., Emery, M., Ledoux, M., Yor, M. (eds.) Séminaire de Probabilités XXXVII. Lecture Notes in Math., vol. 1832, pp. 415-446. Springer, Berlin (2003)
17. Del Moral, P., Miclo, L.: Branching and interacting particle systems approximations of Feynman-Kac formulae with applications to non-linear filtering. In: Séminaire de Probabilitiés XXXIV. Lecture Notes in Math., vol. 1729, pp. 1-145. Springer, Berlin (2000)
18. Del Moral, P., Doucet, A., Jasra, A.: Sequential Monte Carlo samplers. J. Roy. Stat. Soc. Ser. B 68, 411-436 (2006a)
19. Del Moral, P., Doucet, A., Jasra, A.: Sequential Monte Carlo for Bayesian computation (with discussion). In: Bayarri, S., Berger, J.O., Bernardo, J.M., Dawid, A.P., Heckerman, D., Smith, A.F.M., West, M. (eds.) Bayesian Statistics 8 (2006b, in press)
20. Diaconis, P., Saloff-Coste, L.: Comparison theorems for reversible Markov chains. Ann. Appl. Probab. 3, 696-730 (1993)
21. Douc, R., Moulines, É.: Limit theorems for weighted samples with applications to sequential Monte Carlo methods. Technical Report, Centre de Mathématiques Appliquées, École Polytechnique (2006). Ann. Stat, (to appear)
22. Douc, R., Cappé, O., Moulines, É.: Comparison of resampling schemes for particle filtering. In 4th International Symposium on Image and Signal Processing and Analysis (ISPA) (2005)
23. Douc, R., Guillin, A., Marin, J.M., Robert, C.P.: Convergence of adaptive sampling schemes. Ann. Stat. (2006a, in press)
24. Douc, R., Guillin, A., Marin, J.M., Robert, C.P.: Minimum variance importance sampling via population Monte Carlo. Technical Report, Université Paris-Dauphine (2006b). ESIAM Probab. Stat. (to appear)
25. Doucet, A., Godsill, S., Andrieu, C.: On sequential Monte Carlo sampling for Bayesian filtering. Stat. Comput. 10, 197-208 (2000)
26. Doucet, A., De Freitas, J.F.G., Gordon, N.J.: Sequential Monte Carlo Methods in Practice. Springer, New York (2001)
27. Eberle, A., Marinelli, C.: Convergence of sequential Markov chain Monte Carlo methods I: Non-linear flow of probability measures. Technical Report, Universität Bonn (2006)
28. Fearnhead, P., Meligkotsidou, L.: Filtering methods for mixture models. J. Comput. Graph. Stat. (2007, to appear)
29. Gelman, A., Meng, X.L.: Simulating normalizing constants: from importance sampling to bridge sampling to path sampling. Stat. Sci. 13, 163-185 (1998)
30. Geyer, C.J.: Markov chain maximum likelihood. In: Keramigas, E. (ed.) Computing Science and Statistics: The 23rd Symposium on the Interface, pp. 156-163. Interface Foundation, Fairfax (1991)
31. Geyer, C.J., Thompson, E.A.: Annealing Markov chain Monte Carlo with applications to ancestral inference. J. Am. Stat. Assoc. 90, 909-920 (1995)
32. Gilks, W.R., Roberts, G.O., George, E.I.: Adaptive direction sampling. The Statistician 43, 179-189 (1994)
33. Gilks, W.R., Berzuini, C.: Following a moving target-Monte Carlo inference for dynamic Bayesian models. J. Roy. Stat. Soc. Ser. B 63, 127-146 (2001)
34. Goswami, G.R., Liu, J.S.: On learning strategies for evolutionary Monte Carlo. Stat. Comput. 17, 23-28 (2007)
35. Grassberger, P.: Pruned-enriched Rosenbluth method: simulations of θ polymers of chain length up to 1 000000. Phys. Rev. E 56, 3682-3693 (1997)
36. Green, P.J.: Reversible jump Markov chain Monte Carlo computation and Bayesian model determination. Biometrika 82, 711-732 (1995)
37. Green, P.J., Mira, A.: Delayed rejection in reversible jump Metropolis-Hastings. Biometrika 88, 1035-1053 (2001)
38. Hammersley, J.M., Morton, K.W.: Poor man's Monte Carlo. J. Roy. Stat. Soc. Ser. B 16, 23-38 (1999)
39. Hastings, W.K.: Monte Carlo sampling methods using Markov chains and their applications. Biometrika 57, 97-109 (1970)
40. Heard, N.A., Holmes, C.C., Stephens, D.A.: A quantitative study of gene regulation involved in the immune response of anopheline mosquitoes: an application of Bayesian hierarchical clustering of curves. J. Am. Stat. Assoc. 101, 18-29 (2006)
41. Hukushima, K., Nemoto, K.: Exchange Monte Carlo method and application to spin glass simulations. J. Phys. Soc. Jpn. 65, 1604-1608 (1996)
42. Iba, Y.: Population Monte Carlo algorithms. Trans. Jpn. Soc. Artif. Intell. 16, 279-286 (2000)
43. Iba, Y.: Extended ensemble Monte Carlo. Int. J. Mod. Phys. 12, 653-656 (2001)
44. Jarzynski, C.: Nonequilibrium equality for free energy differences. Phys. Rev. Lett. 78, 2690-2693 (1997)
45. Jasra, A.: Bayesian inference for mixture models via Monte Carlo computation. PhD thesis, Imperial College London (2005)
46. Jasra, A., Doucet, A.: Stability of sequential Monte Carlo samplers via the Foster-Lyapunov condition. Technical Report, University of British Columbia (2006)
47. Jasra, A., Holmes, C.C., Stephens, D.A.: Markov chain Monte Carlo methods and the label switching problem in Bayesian mixture modelling. Stat. Sci. 20, 50-67 (2005a)
48. Jasra, A., Stephens, D.A., Holmes, C.C.: Population-based reversible jump Markov chain Monte Carlo. Technical Report, Imperial College London (2005b). Biometrika (to appear)
49. Jasra, A., Doucet, A., Stephens, D.A., Holmes, C.C.: Interacting sequential Monte Carlo samplers for trans-dimensional simulation. Technical Report, Imperial College London (2005c)
50. Johansen, A., Del Moral, P., Doucet, A.: Sequential Monte Carlo samplers for rare event estimation. Technical Report, University of Cambridge (2006)
51. Kou, S.C., Zhou, Q., Wong, W.H.: Equi-energy sampler with applications to statistical inference and statistical mechanics. Ann. Stat. 32, 1581-1619 (2006)
52. Künsch, H.R.: Recursive Monte Carlo filters; algorithms and theoretical analysis. Ann. Stat. 33, 1983-2021 (2005)
53. Liang, F.: Dynamically weighted importance sampling in Monte Carlo computation. J. Am. Stat. Assoc. 97, 807-821 (2002)
54. Liang, F.: Use of sequential structure in simulation from high-dimensional systems. Phys. Rev. E 67, 056101-056107 (2003)
55. Liang, F., Wong, W.H.: Real parameter evolutionary Monte Carlo with applications to Bayesian mixture models. J. Am. Stat. Assoc. 96, 653-666 (2001)
56. Liu, J.S.: Monte Carlo Strategies in Scientific Computing. Springer, New York (2001)
57. Liu, J.S., Chen, R.: Sequential Monte Carlo methods for dynamic systems. J. Am. Stat. Assoc. 93, 1032-1044 (1998)
58. Liu, J.S., Chen, R., Wong, W.H.: Rejection control and sequential importance sampling. J. Am. Stat. Assoc. 93, 1022-1031 (1998)
59. Madras, N., Zheng, Z.: On the swapping algorithm. Random Struct. Algorithms 22, 66-97 (2003)
60. Marinari, E., Parisi, G.: Simulated tempering; a new Monte Carlo scheme. Europhys. Lett. 19, 451-458 (1992)
61. Matthews, P.: A slowly mixing Markov chain and its implication for Gibbs sampling. Stat. Probab. Lett. 17, 231-236 (1993)
62. McLachlan, G.J., Peel, D.: Finite Mixture Models. Wiley, Chichester (2000)
63. Metropolis, N., Rosenbluth, A.W., Rosenbluth, M.N., Teller, A.H., Teller, E.: Equations of state calculations by fast computing machines. J. Chem. Phys. 21, 1087-1092 (1953)
64. Mitsutake, A., Sugita, Y., Okamoto, Y.: Replica-exchange multicanonical and multicanonical replica exchange Monte Carlo simulations of peptides. I. Formula and benchmark tests. J. Chem. Phys. 118, 6664-6676 (2003)
65. Neal, R.M.: Sampling from multimodal distributions using tempered transitions. Stat. Comput. 4, 353-366 (1996)
66. Neal, R.M.: Annealed importance sampling. Stat. Comput. 11, 125-139 (2001)
67. Neal, R.M.: Estimating ratios of normalizing constants using linked importance sampling. Technical Report, University of Toronto (2005)
68. Pritchard, J.K., Stephens, M., Donnelly, P.: Inference of population structure using multilocus genotype data. Genetics 155, 945-959 (2001)
69. Richardson, S., Green, P.J.: On Bayesian analysis of mixture models with an unknown number of components (with discussion). J. Roy. Stat. Soc. Ser. B 59, 731-792 (1997)
70. Robert, C.P., Casella, G.: Monte Carlo Statistical Methods, 2nd edn. Springer, New York (2004)
71. Robert, C.P., Rydén, T., Titterington, D.M.: Bayesian inference in hidden Markov models through reversible jump Markov chain Monte Carlo. J. Roy. Stat. Soc. Ser. B 62, 57-75 (2000)
72. Roberts, G.O., Rosenthal, J.S.: General state space Markov chains and MCMC algorithms. Probab. Surv. 1, 20-71 (2004)
73. Roberts, G.O., Rosenthal, J.S.: Coupling and ergodicity of adaptive MCMC Technical Report, University of Lancaster (2005)
74. Ron, D., Swendson, R.H., Brandt, A.: Inverse Monte Carlo renormalization group transformations for critical phenomena. Phys. Rev. Lett. 89, 275701-275705 (2002)
75. Rousset, M.: Continuous time population Monte Carlo and computational physics. PhD thesis, Universitié Paul Sabatier, Toulouse (2006)
76. Rousset, M., Stoltz, G.: Equilibrium sampling from nonequilibrium dynamics. J. Stat. Phys. 123(6), 1251-1272 (2006)
77. Warnes, A.: The normal kernel coupler: an adaptive Markov chain Monte Carlo method for efficiently sampling from multimodal distributions. PhD thesis, University of Washington (2001)
78. Whitley, D.: A genetic algorithm tutorial. Stat. Comput. 4, 65-85 (1994)
79. Wong, W.H., Liang, F.: Dynamic weighting in Monte Carlo optimization. Proc. Nat. Acad. Sci. 94, 14220-14224 (1997)
80. Zhang, J.L., Liu, J.S.: A new sequential importance sampling method and its application to the two dimensional hydrophobic-hydrophilic model. J. Chem. Phys. 117, 3492-3498 (2002)
81. Zheng, Z.: On swapping and simulated tempering algorithms. Stoch. Process. Appl. 104, 131-153 (2003)