On the relationship between markov chain monte carlo methods for model uncertainty

Journal of Computational and Graphical Statistics

Volumn 10, Issue 2, 2001, Pages 230-248

  Godsill, Simon J ^a  

^a UNIVERSITY OF CAMBRIDGE   (United Kingdom)

Author keywords

Bayes; Jump diffusion; Model selection; Reversible jump; Variable selection

Indexed keywords

EID: 0035591051     PISSN: 10618600     EISSN: 15372715     Source Type: Journal    
DOI: 10.1198/10618600152627924     Document Type: Article

References (44)

1. Barbieri, M., and O’Hagan, A. (1996), “A Reversible Jump MCMC Sampler for Bayesian Analysis of ARMA Time Series,” Technical Report, Universita Roma: La Sapienza.
2. Barker, S., andRayner, P. J. W. (1998), “Unsupervised Image Segmentation,”in Proceedings of IEEE International Conference on Acoustics, Speech and SignalProcessing (vol. 5), pp. 2757-2760.
3. Barnett, G., Kohn, R., and Sheather, S. (1996), “Bayesian Estimation of an Autoregressive Model Using Markov Chain Monte Carlo,” Journal of Econometrics, 74, 237-254.
4. Besag, J. (1989), “A Candidate’s Formula-A Curious Result in Bayesian Prediction,” Biometrika, 76, 183.
5. Besag, J. (1997), Discussion of “Bayesian Analysis ofMixtures With an Unknown Number of Components,”by S. Richardson and P. Green, Journal of the Royal StatisticalSociety, Series B, 59, 774.
6. Box, G. E. P., Jenkins, G. M., and Reinsel, G. C. (1994), Time Series Analysis, Forecasting and Control (3rd ed.), EnglewoodCliffs, NJ: Prentice Hall.
7. Brooks, S. P., and Giudici, P. (1999), “Convergence Assessment for Reversible Jump MCMC Simulations,” in Bayesian Statistics 6, eds. J. Bernardo, J. Berger, A. Dawid, and A. Smith, Oxford: Oxford University Press, pp. 733-742.
8. Carlin, B. P., andChib, S. (1995), “Bayesian ModelChoiceviaMarkovChainMonteCarlo,” Journalof theRoyal StatisticalSociety, Series B, 57, 473-484.
9. Carter, C., and Kohn, R. (1996), “Markov Chain Monte Carlo in Conditionally Gaussian State Space Models,” Biometrika, 83, 589-601.
10. Chib, S. (1995), “Marginal Likelihood Fromthe Gibbs Output,” Journal of American Statistical association, 90, 1313-1321.
11. Chib, S., and Greenberg, E. (1998), “Analysis o fMultivariate Probit Models,” Biometrika, 85, 347-361.
12. Clyde, M., Desimone, H., and Parmigiani, G. (1996), “Prediction via Orthogonalized Model Mixing,” Journal of American Statistical Association, 91, 1197-1208.
13. Dellaportas, P., Forster, J., and Ntzoufras, I. (1997), “On Bayesian Model and Variable Selection Using MCMC,” Technical Report, Department of Statistics, Athens University of Economy and Business.
14. Denison, D., Mallick, B., and Smith, A. (1998), “Automatic Bayesian Curve Fitting,” Journal of the Royal Statistical Society, Series B, 60, 333-350.
15. 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.
16. Gelman, A., andRubin, D. (1992), “Inference FromIterativeSimulationsUsing MultipleSequences,” Statistical Science, 7, 457-511.
17. Geman, S., and Geman, D. (1984), “Stochastic Relaxation, Gibbs Distributions and the Bayesian Restoration of Images,” IEEE Transactionson Pattern Analysis and Machine Intelligence, 6, 721-741.
18. George, E. I., and McCulloch, R. E. (1993), “Variable Selection via Gibbs Sampling,” Journal of the American Statistical Association, 88, 881-889.
19. George, E. I., and McCulloch, R. E. (1996), “Approaches for Bayesian Variable Selection,” StatisticaSinica, 7, 339-374.
20. Geweke, J. (1996), “Variable Selection and Model Comparison in Regression,” in Bayesian Statistics V, eds. J. Bernardo, J. Berger, A. Dawid, and A. Smith, Oxford: Oxford University Press, pp. 609-620.
21. Godsill, S. J. (1997), “Bayesian Enhancement of Speech and Audio Signals Which can be Modelled as ARMA Processes,” International Statistical Review, 65, 1-21.
22. Godsill, S. J., and Rayner, P. J. W. (1996), “Robust Treatment of Impulsive Noise in Speech and Audio Signals,” in Bayesian Robustness-Proceedings of the Workshop on Bayesian Robustness (vol. 29), eds. J. Berger, B. Betro, E. Moreno, L. Pericchi, F. Ruggeri, G. Salinetti, and L. Wasserman, Hayward, CA: IMS, pp. 331-342.
23. Godsill, S. J., and Rayner, P. J. W. (1998), “Robust Reconstruction and Analysis of Autoregressive Signals in Impulsive Noise Using the Gibbs Sampler,” IEEE Transactionson Speech andAudioProcessing, 6, 352-372.
24. Green, P., and O’Hagan, A. (1997), “Carlin and Chib do not Need to Sample FromPseudo-Priors,” unpublished report.
25. Green, P. J. (1995), “Reversible Jump Markov-Chain Monte Carlo Computation and Bayesian Model Determina tion,” Biometrika, 82, 711-732.
26. Grenander, U., and Miller, M. I. (1991), “Jump-DiffusionProcesses for Abduction and RecognitionofBiological Shapes,” Technical Report, Electronic Signals and Systems Research Laboratory, Washington University.
27. Grenander, U., and Miller, M. I. (1994) “Representations of Knowledge in Complex Systems,” Journal of the Royal Statistical Society, Series B, 56, 549-603.
28. Hastings, W. K. (1970), “Monte Carlo Sampling Methods Using Markov Chains and Their Applications,” Biometrika, 57, 97-109.
29. Hoeting, J., Raftery, A., and Madigan, D. (1996), “A Method for Simultaneous Variable Selection and Outlier Identification in Linear-Regression,” ComputationalStatistics and Data Analysis, 22, 251-270.
30. Huerta, G., and West, M. (1999), “Priors and Component Structures in Autoregressive Time Series Models,” Journal of the RoyalStatisticalSociety, Series B, 61, 881-899.
31. Kuo, L., and Mallick, B. (1998), “Variable Selection for Regression Models,” Sankhya, Series B, 60, 65-81.
32. Madigan, D., and York, J. (1995), “Bayesian Graphical Models for Discrete Data,” International Statistical Review, 63, 215-232.
33. McCulloch, R. E., and Tsay, R. S. (1994), “Bayesian Analysis of Autoregressive Time Series via the Gibbs Sampler,” Journalof Time Series Analysis, 15, 235-250.
34. Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N., Teller, A. H., and Teller, E. (1953), “Equations of State Calculations by Fast Computing Machines,” Journal ofChemical Physics, 21, 1087-1091.
35. Morris, R. D., Fitzgerald, W. J., and Kokaram, A. C. (1996), “A Sampling Based Approach to Line Scratch RemovalFromMotionPictureFrames,” inProceedings IEEE International Conferenceon Image Processing, Lausanne, Switzerland.
36. Phillips, D. B., and Smith, A. F. M. (1994), “Bayesian Model ComparisonviaJump Diffusions,” Technical Report TR-94-20, Imperial College.
37. Raftery, A. (1996), “Hypothesis Testing and Model Selection,” in Markov Chain Monte Carlo in Practice, eds. W. R. Gilks, S. Richardson, and D. J. Spiegelhalter, London: Chapman and Hall, pp. 163-187.
38. Raftery, A., Madigan, D., and Hoeting, J. (1997), “Bayesian Model Averaging for Linear Regression Models,” Journal of the American Statistical Association, 92, 179-191.
39. Richardson, S., andGreen, P. (1997), “Bayesian Analysis ofMixturesWithanUnknownNumberof Components,” Journal of the RoyalStatisticalSociety, Series B, 59, 731-758.
40. Robert, C., and Casella, G. (1999), Monte Carlo StatisticalMethods, New York: SpringerVerlag.
41. Stark, J., Fitzgerald, W., and Hladky, S. (1997), “Multiple-Order Markov Chain Monte Carlo Sampling Methods with Application to a Changepoint Model,” Technical Report CUED/F-INFENG/TR. 302, Department of Engineering, University of Cambridge.
42. Troughton, P., and Godsill, S. J. (1998), “A Reversible Jump Sampler for Autoregressive Time Series,” in Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing (vol. IV), pp. 2257-2260.
43. Troughton, P., and Godsill, S. J. (2001), “MCMC Methods for Restoration of Nonlinearly Distorted Autoregressive Signals,” Signal Processing, 81, 83-97.
44. West, M., and Harrison, J. (1997), Bayesian Forecasting and Dynamic Models (2nd ed.), New York: Springer Verlag