Estimating ratios of normalizing constants for densities with different dimensions

Statistica Sinica

Volumn 7, Issue 3, 1997, Pages 607-630

  Chen, Ming Hui ^a,b   Shao, Qi Man ^a  

^a UNIVERSITY OF OREGON   (United States)

^b WORCESTER POLYTECHNIC INSTITUTE   (United States)

Author keywords

Bayes factor; Bayesian computation; Bridge sampling; Gibbs sampler; Importance sampling; Markov chain Monte Carlo; Metropolis algorithm; Ratio importance sampling

Indexed keywords

EID: 0031492218     PISSN: 10170405     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (35)

1. Albert, J. H. and Chib, S. (1993). Bayesian analysis of binary and polychotomous response data. J. Amer. Statist. Assoc. 88, 669-679.
2. Berger, J. O. and Pericchi (1996). The intrinsic Bayes factor for model selection and prediction. J. Amer. Statist. Assoc. 91, 109-122.
3. Besag, J. and Green, P. J. (1993). Spatial statistics and Bayesian computation. J. Roy. Statist. Soc. Ser. B 55, 25-37.
4. Carlin, B. P. and Chib, S. (1995). Bayesian model choice via Markov chain Monte Carlo methods. J. Roy. Statist. Soc. Ser. B 57, 473-484.
5. Chen. M.-H. (1994). Importance-weighted marginal Bayesian posterior density estimation. J. Amer. Statist. Assoc. 89, 818-824.
6. Chen, M.-H. and Schmeiser, B. W. (1994). Random-direction interior-point Markov chains: a family of black-box samplers. Proceedings of the Section on Bayesian Statistical Science. American Statistical Association, Toronto, Canada, 1-6.
7. Chen, M.-H. and Schmeiser, B. W. (1993). Performance of the Gibbs, hit-and-run, and Metropolis samplers. The J. Comput. Graph. Statist. 2, 251-272.
8. Chen, M.-H. and Shao, Q. M. (1997). On Monte Carlo methods for estimating ratios of normalizing constants. Ann. Statist. 25, in press.
9. Chib, S. (1995). Marginal likelihood from the Gibbs output. J. Amer. Statist. Assoc. 90, 1313-1321.
10. Cowles, M. K. and Carlin, B. P. (1996). Markov chain Monte Carlo convergence diagnostics: a comparative review. J. Amer. Statist. Assoc. 91, 883-904.
11. Dey, D. K. and Chen, M.-H. (1996). Bayesian analysis of correlated binary data models. Technical report 96-02, Department of Statistics, University of Connecticut.
12. Gelfand, A. E. and Smith, A. F. M. (1990). Sampling-based approaches to calculating marginal densities. J. Amer. Statist. Assoc. 85, 398-409.
13. Gelfand, A. E., Smith, A. F. M. and Lee, T. M. (1992). Bayesian analysis of constrained parameter and truncated data problems using Gibbs sampling. J. Amer. Statist. Assoc. 87, 523-532.
14. Gelman, A. and Meng, X.-L. (1994). Path sampling for computing normalizing constants: identities and theory. Technical Report 377, Department of Statistics, The University of Chicago.
15. Geman, S. and Geman, D. (1984). Stochastic relaxation, Gibbs distributions and the Bayesian restoration of images. IEEE Trans. Pattern Anal. Machine Intelligence 6, 721-741.
16. Geweke, J. (1989). Bayesian inference in econometrics models using Monte Carlo integration. Econometrica 57, 1317-1339.
17. Geweke, J. (1994). Bayesian comparison of econometric models. Technical Report 532, Federal Reserve Bank of Minneapolis and University of Minnesota.
18. Geyer, C. J. (1994). Estimating normalizing constants and reweighting mixtures in Markov chain Monte Carlo. Revision of Technical Report No. 568, School of Statistics, University of Minnesota.
19. Gilks, W. R. and Wild, P. (1992). Adaptive rejection sampling for Gibbs sampling. Appl. Statist. 41, 337-348.
20. Hastings, W. K. (1970). Monte Carlo sampling methods using Markov chains and their applications. Biometrika 57, 97-109.
21. Ibrahim, J. G., Chen, M.-H. and MacEachern, S. N. (1996). Bayesian variable selection for proportional hazards models. Technical Report, Department of Biostatistics, Harvard School of Public Health.
22. Jeffreys, H. (1961). Theory of Probability. Third Edition. Clarendon Press: Oxford.
23. Kass, R. E. and Raftery, A. E. (1995). Bayes factor. J. Amer. Statist. Assoc. 90, 773-795.
24. Laud, P. W. and Ibrahim, J. G. (1996). Predictive specification of prior model probabilities in variable selection. Biometrika 83, 267-274.
25. 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.
26. Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N., Teller, A. H. and Teller, E. (1953). Equations of state calculations by fast computing machines. J. Chem. Phys. 21, 1087-1092.
27. Müller, P. (1991). A generic approach to posterior integration and Gibbs sampling. Technical Report #91-09, Department of Statistics, Purdue University.
28. Newton, M. A. and Raftery, A. E. (1994). Approximate Bayesian inference with the weighted likelihood bootstrap (with discussion). J. Roy. Statist. Soc. Ser. B 56, 3-48.
29. Polson, N. G. (1996). Convergence of Markov chain Monte Carlo algorithms. In Bayesian Statistics 5 (Edited by J. M. Bernado, J. O. Berger, A. P. Dawid and A. F. M. Smith), 297-322. Oxford University Press.
30. Ritter, C. and Tanner, M. A. (1992). Facilitating the Gibbs sampler: the Gibbs stopper and the griddy-Gibbs sampler. J. Amer. Statist. Assoc. 87, 861-868.
31. Schervish, M. J. and Carlin, B. P. (1992). On the convergence of successive substitution sampling. J. Comput. Graphical Statist. 1, 111-127.
32. Tanner, M. A. and Wong, W. H. (1987). The calculation of posterior distributions by data augmentation. J. Amer. Statist. Assoc. 82, 528-550.
33. Tierney, L. (1994). Markov chains for exploring posterior distributions (with discussion). Ann. Statist. 22, 1701-1762.
34. Verdinelli, I. and Wasserman, L. (1995). Computing Bayes factors using a generalization of the Savage-Dickey density ratio. J. Amer. Statist. Assoc. 90, 614-618.
35. Verdinelli, I. and Wasserman, L. (1996). Bayes factors, nuisance parameters and imprecise tests. In Bayesian Statistics 5 (Edited by J. M. Bernado, J. O. Berger, A. P. Dawid and A. F. M. Smith ), 765-772. Oxford University Press.