Computational advances for and from Bayesian analysis

Statistical Science

Volumn 19, Issue 1, 2004, Pages 118-127

  Andrieu, C ^a   Doucet, A ^b   Robert, C P ^c  

^a UNIVERSITY OF BRISTOL   (United Kingdom)

^b UNIVERSITY OF CAMBRIDGE   (United Kingdom)

^c UNIVERSITÉ PARIS DAUPHINE   (France)

Author keywords

Importance sampling; Markov chain Monte Carlo (MCMC) algorithms; Monte Carlo methods

Indexed keywords

EID: 4043091425     PISSN: 08834237     EISSN: None     Source Type: Journal    
DOI: 10.1214/088342304000000071     Document Type: Review

References (71)

1. ANDRIEU, C. and DOUCET, A. (1999). Joint Bayesian model selection and estimation of noisy sinusoids via reversible jump MCMC. IEEE Trans. Signal Process. 47 2667-2676.
2. ANDRIEU, C. and ROBERT, C. (2001). Controlled MCMC for optimal sampling. Technical Report 0125, CEREMADE, Université Paris Dauphine.
3. BAYARRI, M. and BERGER, J. (2004). The interplay of Bayesian and frequentist analysis. Statist. Sci. 19 58-80.
4. BERGER, J. and PERICCHI, L. (1996). The intrinsic Bayes factor for model selection and prediction. J. Amer. Statist. Assoc. 91 109-122.
5. BERGER, J. and PERICCHI, L. (2001). Objective Bayesian methods for model selection: Introduction and comparison (with discussion). In Model Selection (P. Lahiri, ed.) 135-207. IMS, Beachwood, OH.
6. BERRY, D. (2004). Bayesian statistics and the efficiency and ethics of clinical trials. Statist. Sci. 19 175-187.
7. BROOKS, S., GIUDICI, P. and ROBERTS, G. (2003). Efficient construction of reversible jump Markov chain Monte Carlo proposal distributions (with discussion). J. R. Stat. Soc. Ser. B Stat. Methodol. 65 3-55.
8. CAPPÉ, O., GUILLIN, A., MARIN, J. and ROBERT, C. (2004). Population Monte Carlo. J. Comput. Graph. Statist. To appear.
9. CAPPÉ, O., MOULINES, E. and RYDÉN, T. (2004). Hidden Markov Models. Springer, New York. To appear.
10. CAPPÉ, O. and ROBERT, C. (2000). Markov chain Monte Carlo: 10 years and still running! J. Amer. Statist. Assoc. 95 1282-1286.
11. CARLIN, B. and CHIB, S. (1995). Bayesian model choice via Markov chain Monte Carlo. J. Roy. Statist. Soc. Ser. B 57 473-484.
12. CASELLA, G., LAVINE, M. and ROBERT, C. (2001). Explaining the perfect sampler. Amer. Statist. 55 299-305.
13. CELEUX, G., MARIN, J. and ROBERT, C. (2003). Iterated importance sampling in missing data problems. Technical report, CEREMADE, Université Paris Dauphine.
14. CHEN, M. and SHAO, Q. (1997). On Monte Carlo methods for estimating ratios of normalizing constants. Ann. Statist. 25 1563-1594.
15. CHEN, M., SHAO, Q. and IBRAHIM, J. (2000). Monte Carlo Methods in Bayesian Computation. Springer, New York.
16. CHOPIN, N. (2002). A sequential particle filter method for static models. Biometrika 89 539-551.
17. CLYDE, M. and GEORGE, E. (2004). Model uncertainty. Statist. Sci. 19 81-94.
18. DEL MORAL, P. and DOUCET, A. (2002). Sequential Monte Carlo samplers. Technical Report 443 CUED/F-INFENG, Dept. Electrical Engineering, Cambridge Univ.
19. DEL MORAL, P. and GIONNET, A. (2001). On the stability of interacting processes with applications to filtering and genetic algorithms. Ann. Inst. H. Poincaré Anal. Non Linéaire 37 155-194.
20. DEMPSTER, A., LAIRD, N. and RUBIN, D. (1977). Maximum likelihood from incomplete data via the EM algorithm (with discussion). J. Roy. Statist. Soc. Ser. B 39 1-38.
21. DOUCET, A., DE FREITAS, N. and GORDON, N., eds. (2001). Sequential Monte Carlo Methods in Practice. Springer, New York.
22. DOUCET, A., GODSILL, S. and ROBERT, C. (2002). Marginal maximum a posteriori estimation using Markov chain Monte Carlo. Statist. Comput. 12 77-84.
23. FOSS, S. and TWEEDIE, R. (1998). Perfect simulation and backward coupling. Comm. Statist. Stochastic Models 14 187-203.
24. GELFAND, A. and SMITH, A. (1990). Sampling-based approaches to calculating marginal densities. J. Amer. Statist. Assoc. 85 398-409.
25. GELMAN, A. and MENG, X. (1998). Simulating normalizing constants: From importance sampling to bridge sampling to path sampling. Statist. Sci. 13 163-185.
26. GEMAN, S. and GEMAN, D. (1984). Stochastic relaxation, Gibbs distributions and the Bayesian restoration of images. IEEE Trans. Pattern Analysis and Machine Intelligence 6 721-741.
27. GILKS, W., RICHARDSON, S. and SPIEGELHALTER, D., eds. (1996). Markov Chain Monte Carlo in Practice. Chapman and Hall, London.
28. GILKS, W., ROBERTS, G. and SAHU, S. (1998). Adaptive Markov chain Monte Carlo through regeneration. J. Amer. Statist. Assoc. 93 1045-1054.
29. GODSILL, S. J. (2001). On the relationship between Markov chain Monte Carlo methods for model uncertainty. J. Comput. Graph. Statist. 10 230-248.
30. GREEN, P. (1995). Reversible jump Markov chain Monte Carlo computation and Bayesian model determination. Biometrika 82 711-732.
31. GUIHENNEUC-JOUYAUX, C. and ROBERT, C. (1998). Discretization of continuous Markov chains and Markov chain Monte Carlo convergence assessment. J. Amer. Statist. Assoc. 93 1055-1067.
32. HAARIO, H., SAKSMAN, E. and TAMMINEN, J. (1999). Adaptive proposal distribution for random walk Metropolis algorithm. Comput. Statist. 14 375-395.
33. HAARIO, H., SAKSMAN, E. and TAMMINEN, J. (2001). An adaptive Metropolis algorithm. Bernoulli 7 223-242.
34. HAMMERSLEY, J. and HANDSCOMB, D. (1964). Monte Carlo Methods. Wiley, New York.
35. HASTINGS, W. (1970). Monte Carlo sampling methods using Markov chains and their applications. Biometrika 57 97-109.
36. HODGSON, M. (1999). A Bayesian restoration of an ion channel signal. J. R. Stat. Soc. Ser. B Stat. Methodol. 61 95-114.
37. IBA, Y. (2000). Population-based Monte Carlo algorithms. Trans. Japanese Society for Artificial Intelligence 16 279-286.
38. JORDAN, M. I. (2004). Graphical models. Statist. Sci. 19 140-155.
39. KASS, R. and RAFTERY, A. (1995). Bayes factors. J. Amer. Statist. Assoc. 90 773-795.
40. KIEFER, J. and WOLFOWITZ, J. (1952). Stochastic estimation of the maximum of a regression function. Ann. Math. Statist. 23 462-466.
41. KIM, S., SHEPHARD, N. and CHIB, S. (1998). Stochastic volatility: Likelihood inference and comparison with ARCH models. Rev. Econom. Stud. 65 361-393.
42. KIRKPATRICK, S., GELATT, C. and VECCHI, M. (1983). Optimization by simulated annealing. Science 220 671-680.
43. LIU, J. (2001). Monte Carlo Strategies in Scientific Computing. Springer, New York.
44. MADIGAN, D. and RAFTERY, A. (1994). Model selection and accounting for model uncertainty in graphical models using Occam's window. J. Amer. Statist. Assoc. 89 1535-1546.
45. MENG, X. and RUBIN, D. (1993). Maximum likelihood estimation via the ECM algorithm: A general framework. Biometrika 80 267-278.
46. MENG, X. and VAN DYK, D. (1997). The EM algorithm - an old folk-song sung to a fast new tune (with discussion). J. Roy. Statist. Soc. Ser. B 59 511-567.
47. MENG, X. and WONG, W. (1996). Simulating ratios of normalizing constants via a simple identity: A theoretical exploration. Statist. Sinica 6 831-860.
48. METROPOLIS, N., ROSENBLUTH, A., ROSENBLUTH, M., TELLER, A. and TELLER, E. (1953). Equations of state calculations by fast computing machines. J. Chemical Physics 21 1087-1092.
49. MIRA, A., MØLLER, J. and ROBERTS, G. (2001). Perfect slice samplers. J. R. Stat. Soc. Ser. B Stat. Methodol. 63 593-606.
50. MÜLLER, P. (1999). Simulation-based optimal design. In Bayesian Statistics 6 (J. Bernardo, J. Berger, A. Dawid, and A. Smith, eds.) 459-474. Oxford Univ. Press.
51. MYKLAND, P., TIERNEY, L. and YU, B. (1995). Regeneration in Markov chain samplers. J. Amer. Statist. Assoc. 90 233-241.
52. NEAL, R. (2001). Annealed importance sampling. Statist. Comput. 11 125-139.
53. NEAL, R. (2003). Slice sampling (with discussion). Ann. Statist. 31 705-767.
54. NEWTON, M. and RAFTERY, A. (1994). Approximate Bayesian inference with the weighted likelihood boostrap (with discussion). J. Roy. Statist. Soc. Ser. B. 56 3-48.
55. OH, M. and BERGER, J. (1993). Integration of multimodal functions by Monte Carlo importance sampling. J. Amer. Statist. Assoc. 88 450-456.
56. PRESTON, C. (1976). Spatial birth-and-death processes. Bull. Internat. Statist. Inst. 46 371-391.
57. PROPP, J. and WILSON, D. (1996). Exact sampling with coupled Markov chains and applications to statistical mechanics. Random Structures Algorithms 9 223-252.
58. RIPLEY, B. (1977). Modelling spatial patterns (with discussion). J. Roy. Statist. Soc. Ser. B 39 172-212.
59. RIPLEY, B. (1987). Stochastic Simulation. Wiley, New York.
60. ROBBINS, H. and MONRO, S. (1951). A stochastic approximation method. Ann. Math. Statist. 22 400-407.
61. ROBERT, C. (2001). The Bayesian Choice, 2nd ed. Springer, New York.
62. ROBERT, C. and CASELLA, G. (1999). Monte Carlo Statistical Method. Springer, New York.
63. ROBERT, C. and CASELLA, G. (2004). Monte Carlo Statistical Methods, 2nd ed. Springer, New York.
64. ROBERTS, G., PAPASPILIOPOULOS, O. and DELLAPORTAS, P. (2001). Bayesian inference for non-Gaussian Ornstein-Uhlenbeck. Technical report, Univ. Lancaster.
65. ROBERTS, G. and ROSENTHAL, J. (1999). Convergence of slice sampler Markov chains. J. R. Stat. Soc. Ser. B Stat. Methodol. 61 643-660.
66. ROBERTS, G. and TWEEDIE, R. (2004). Understanding MCMC. Springer, New York. To appear.
67. SMITH, A. and ROBERTS, G. (1993). Bayesian computation via the Gibbs sampler and related Markov chain Monte Carlo methods (with discussion). J. Roy. Statist. Soc. Ser. B 55 3-23.
68. STEPHENS, M. (2000). Bayesian analysis of mixture models with an unknown number of components - An alternative to reversible jump methods. Ann. Statist. 28 40-74.
69. TANNER, M. and WONG, W. (1987). The calculation of posterior distributions by data augmentation (with discussion). J. Amer. Statist. Assoc. 82 528-550.
70. TITTERINGTON, D. M. (2004). Bayesian methods for neural networks and related models. Statist. Sci. 19 128-139.
71. WALKER, S. (2004). Modern Bayesian asymptotics. Statist. Sci. 19 111-117.