Metropolized independent sampling with comparisons to rejection sampling and importance sampling

Statistics and Computing

Volumn 6, Issue 2, 1996, Pages 113-119

  Liu, Jun S ^a  

^a STANFORD UNIVERSITY   (United States)

Author keywords

Coupling; Delta method; Eigen analysis; Importance ratio

Indexed keywords

EID: 21344458535     PISSN: 09603174     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF00162521     Document Type: Article

References (22)

1. Besag, J. and Green, P.J. (1993). Spatial statistics and Baysian computation. Journal of the Royal Statistical Society B, 55, 24-35.
2. Diaconis, P. (1988) Group Representations in Probability and Statistics, Lecture Notes-Monograph Series 11, IMS, Hayward, California.
3. Diaconis, P. and Hanlon, P. (1992) Eigen analysis for some examples of the Metropolis algorithm. Contemporary Mathematics, 138, 99-117.
4. 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.
5. Gelman, A. and Rubin, D. B. (1993) Discussion on Gibbs sampler and other MCMC methods. Journal of the Royal Statistical Society B, 55, 73-73.
6. 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, 721-41.
7. Hastings, W. K. (1970) Monte Carlo sampling methods using Markov chains and their applications. Biometrika, 57, 97-109.
8. Kong, A. (1992) A note on importance sampling using renormalized weights. Technical report, Department of Statistics, University of Chicago.
9. Lindvall, T. (1992) Lectures on the Coupling Method. Wiley, New York.
10. Liu, J. S. (1994) The collapsed Gibbs sampler in Bayesian computations with applications to a gene regulation problem. Journal of the American Statistical Association, 89, 958-66.
11. Liu, J. S., Kong, A. and Wong, W. H. (1994) Covariance structure of the Gibbs sampler with applications to the comparisons of estimators and augmentation schemes. Biometrika, 81, 27-40.
12. Lovasz, L. and Simonovits, M. (1990) The mixing rate of Markov chains, an isoperimetric inequality, and computing the volume. Preprint 27, Hungarian Academy of Sciences.
13. Marshall, A. W. (1956) The use of multi-stage sampling schemes in Monte Carlo computations. In Symposium on Monte Carlo Methods, ed. M. A. Meyer, pp. 123-40, Wiley, New York.
14. Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N., Teller, A. H. and Teller, E. (1953) Equations of state calculations by fast computing machines. Journal of Chemical Physics, 21, 1087-91.
15. von Neumann, J. (1951) Various techniques used in connection with random digits. National Bureau of Standards Applied Mathematics Series, 12, 36-8.
16. Peskun, P. H. (1973) Optimum Monte-Carlo sampling using Markov chains. Biometrika, 60, 607-12.
17. Rosenthal, J. S. (1995) Rates of convergence for Gibbs sampler for variance components models. Ann. Statist., 23, 740-61.
18. Smith, A. F. M. and Roberts, G. O. (1993) Bayesian Computation via the Gibbs sampler and related Markov chain Monte Carlo methods. Journal of the Royal Statistical Society, B, 55, 3-23.
19. Smith, R. L. (1994) Exact transition probabilities for Metropolized independent sampling. Technical Report, Dept. Statistics, Univ. of North Carolina.
20. Tanner, M. A. and Wong, W. H. (1987) The calculation of posterior distributions by data augmentation (with discussion). Journal of American Statistical Association, 82, 528-50.
21. Tierney, L. (1991) Markov chains for exploring posterior distributions. In Computer Science and Statistics: Proc. 23rd Symp. Interface.
22. Yoida, K. (1978) Functional Analysis. Springer-Verlag, New York.