On Monte Carlo methods for estimating ratios of normalizing constants

Annals of Statistics

Volumn 25, Issue 4, 1997, Pages 1563-1594

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

^a Worcester Polytechnic Institute   (United States)

^b UNIVERSITY OF OREGON   (United States)

Author keywords

Bayesian computation; Bridge sampling; Gibbs sampling; Importance sampling; Markov chain Monte Carlo; Metropolis Hastings algorithm; Path sampling; Ratio importance sampling

Indexed keywords

EID: 0031527297     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/aos/1031594732     Document Type: Article

References (23)

1. BERGER, J. O. and PERICCHI, L. R. (1996). The intrinsic Bayes factor for model selection and prediction. J. Amer. Statist. Assoc. 91 109-122.
2. CHEN, M.-H. (1994a). Simulating ratios of normalization constants for the Gibbs Sampler. Technical report, Dept. Mathematical Sciences, Worcester Polytechnic Inst.
3. CHEN, M.-H. (1994b). Importance-weighted marginal Bayesian posterior density estimation. J. Amer. Statist. Assoc. 89 818-824.
4. CHEN, M.-H. and SCHMEISER, B. W. (1993). Performance of the Gibbs, hit-and-run, and Metropolis samplers. J. Comput. Graph. Statist. 2 251-272.
5. CHIB, S. (1995). Marginal likelihood from the Gibbs output. J. Amer. Statist. Assoc. 90 1313-1321.
6. DEVROYE, L. (1986). Non-Uniform Random Variate Generation. Springer, New York.
7. GELFAND, A. E. and SMITH, A. F. M. (1990). Sampling based approaches to calculating marginal densities. J. Amer. Statist. Assoc. 85 398-409.
8. 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.
9. GELMAN, A. and MENG, X.-L. (1994). Path sampling for computing normalizing constants: identities and theory. Technical Report 377, Dept. Statistics, Univ. Chicago.
10. GELMAN, A. and MENG, X.-L. (1996). Simulating normalizing constants: from importance sampling to bridge sampling to path sampling. Technical Report 440, Dept. Statistics, Univ. Chicago.
11. 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.
12. GEWEKE, J. (1989). Bayesian inference in econometrics models using Monte Carlo integration. Econometrica 57 1317-1340.
13. GEWEKE, J. (1994). Bayesian comparison of econometric models. Technical Report 532, Federal Reserve Bank of Minneapolis and Univ. Minnesota.
14. GEYER, C. J. (1994). Estimating normalizing constants and reweighting mixtures in Markov chain Monte Carlo. Rev. Technical Report 568, School of Statistics, Univ. Minnesota.
15. GREEN, P. J. (1992). Discussion of "Constrained Monte Carlo maximum likelihood for dependent data," by C. J. Geyer and E. A. Thompson. J. Roy. Statist. Soc. Ser. B 54 657-699.
16. HASTINGS, W. K. (1970). Monte Carlo sampling methods using Markov chains and their applications. Biometrika 57 97-109.
17. HE, X. and SHAO, Q. M. (1996). A general Bahadur representation of M-estimators and its application to linear regression with nonstochastic designs. Ann. Statist. 24 2608-2630.
18. JANSSEN, P., JURECKOVA, J. and VERAVERBEKE, N. (1985). Rate of convergence of one- and two-step M-estimators with applications to maximum likelihood and Pitman estimators. Ann. Statist. 13 1222-1229.
19. 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.
20. 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.
21. MÜLLER, P. (1991). A generic approach to posterior integration and Gibbs sampling. Technical Report #91-09, Dept. Statistics, Purdue Univ.
22. TANNER, M. A. and WONG, W. H. (1987). The calculation of posterior distributions by data augmentation. J. Amer. Statist. Assoc. 82 528-549.
23. TIERNEY, L. (1994). Markov chains for exploring posterior distributions (with discussion). Ann. Statist. 22 1701-1762.