A coupling-regeneration scheme for diagnosing convergence in markov chain monte carlo algorithms

Journal of the American Statistical Association

Volumn 93, Issue 441, 1998, Pages 238-248

  Johnson, Valen E ^a  

^a DUKE UNIVERSITY   (United States)

Author keywords

Gibbs sampling; Hastings algorithms; Maximal coupling; Metropolis algorithm; Regeneration and coupling

Indexed keywords

EID: 0032343818     PISSN: 01621459     EISSN: 1537274X     Source Type: Journal    
DOI: 10.1080/01621459.1998.10474105     Document Type: Article

References (36)

1. Athreya, K. B., and Ney, P. (1978), "A New Approach to the Limit Theory of Recurrent Markov Chains," Transactions of the American Mathematical Society, 245, 493-501.
2. Besag, J., and Green, P. (1993), "Spatial Statistics and Bayesian Computation" (with discussion), Journal of the Royal Statistical Society, Ser. B, 55, 25-37.
3. Besag, J., Green, P., Higdon, D., and Mengerson, K. (1995), "Bayesian Computation and Stochastic Systems" (with discussion), Statistical Science, 10, 3-66.
4. Cox, D. R., and Snell, E. J. (1989), Analysis of Binary Data (2nd ed.) London: Chapman and Hall.
5. Frigessi, A., Hwang, C. R., and Younes, L. (1992), "Convergence Rates of the Gibbs Sampler, the Metropolis Algorithm and Other Single-Site Updating Dynamics," Journal of the Royal Statistical Society, Ser. B, 55, 205-219.
6. Garren, S. T., and Smith, R. L. (1994), "Convergence Diagnostics for Markov Chain Samplers," preprint, University of North Carolina.
7. Gelfand, A. E., Hills, S. E., Racine-Poon, A., and Smith, A. F. M. (1990), "Illustration of Bayesian Inference in Normal Data Models Using Gibbs SamplingJournal of the American Statistical Association, 85,972-985.
8. 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.
9. Gelman, A., and Rubin, D. B. (1992), "Inference From Iterative Simulation," Statistical Science, 7, 457-472.
10. 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.
11. Geyer, C. (1992), "Practical Markov Chain Monte Carlo," Statistical Science, 1, 473-483.
12. Goldstein, S. (1979), "Maximal Coupling," Zeitschrift für Wahrsheinlichkeitstheorie und Verwandte Gebiete, 46, 193-204.
13. Griffeath, D. (1975), "A Maximal Coupling for Markov Chains," Zeitschrift für Wahrsheinlichkeitstheorie und Verwandte Gebiete, 31, 95-106.
14. Johnson, V. E. (1996), "Studying Convergence of Markov Chain Monte Carlo Algorithms Using Coupled Sample Paths," Journal of the American Statistical Association, 91, 154-166.
15. Lindvall, T. (1992), Lectures on the Coupling Method, New York: Wiley.
16. Lund, R. B., and Tweedie, R. L. (1993), "Geometric Convergence Rates for Stochastically Ordered Markov Chains," Technical Report, Colorado State University, Dept, of Statistics.
17. Meyn, S. P., and Tweedie, R. L. (1993). "Computable Bounds for Convergence Rates of Markov Chains," Technical Report, Colorado State University, Dept, of Statistics.
18. Murdoch, D. J., and Green, P. J. (1997), "Exact Sampling from a Continuous State Space," Technical Report, Queens University, Ontario, Dept, of Mathematics and Statistics.
19. Mykland, C., Tierney, L., and Yu, B. (1995), "Regeneration in Markov Chain Samplers," Journal of the American Statistical Association, 90, 233-241.
20. Nummelin, E. (1978), "A Splitting Technique for Harris Recurrent Markov Chains," Zeitschrift für Wahrsheinlichkeitstheorie und Verwandte Gebiete, 43, 309-318.
21. Nummelin, E. (1984), General Irreducible Markov Chains and Nonnegative Operators, Cambridge, U.K.: Cambridge University Press.
22. Pitman, J. W. (1976), "On Coupling of Markov Chains," Zeitschrift für Wahrsheinlichkeitstheorie und Verwandte Gebiete, 35, 315-322.
23. Pickard, D. (1987), "Inference for Discrete Markov Fields: The Simplest Nontrivial Case," Journal of the American Statistical Association, 82, 90-96.
24. Propp, J. G., and Wilson, B. M. (1995), "Exact Sampling With Coupled Markov Chains and Applications to Statistical Mechanics," Technical Report, Massachusetts Institute of Technology, Dept, of Mathematics.
25. Raftery, A. E., and Lewis, S. M. (1992), "How Many Iterations of the Gibbs Sampler?," in Bayesian Statistics 4: Proceedings of the Fourth Valencia International Meeting, eds. Bernardo, Berger, Dawid, and Smith, Oxford, U.K.: Oxford University Press.
26. Reutter, A., and Johnson, V. E. (1995), "General Strategies for Assessing Convergence of MCMC Algorithms Using Coupled Sample Paths," ISDS Discussion Paper 95-25, Duke University.
27. Roberts, G. O. (1992), "Convergence Diagnostics of the Gibbs Sampler," in Bayesian Statistics 4, eds. Bernardo, Berger, Dawid, and Smith, Oxford, U.K.: Oxford University Press, pp. 777-784.
28. Roberts, G. O., and Hills, S. E. (1992), "Assessing Distributional Convergence of the Gibbs Sampler," preprint, University of Cambridge.
29. Roberts, G. O., and Poison, N. G. (1994), "On the Geometric Convergence of the Gibbs Sampler," Journal of the Royal Statistical Society, Ser. B, 56, 377-384.
30. Roberts, G. O., and Tweedie, R. L. (1996), "Geometric Convergence and Central Limit Theorems for Multidimensional Hastings and Metropolis Algorithms," Biometrika, 83, 95-110.
31. Rosenthal, J. S. (1995), "Minorization Conditions and Convergence Rates for Markov Chain Monte Carlo," Journal of the American Statistical Association, 90, 558-566.
32. Ruelle, D. (1969), Statistical Mechanics, New York: Benjamin.
33. 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, Ser. B, 55, 3-23.
34. Tanner, M. and Wong, W. H. (1987). 'The Calculation of Posterior Distributions by Data Augmentation" (with discussion), Journal of the American Statistical Association, 82, 528-550.
35. Tierney, L. (1994), "Markov Chains for Exploring Posterior Distributions" (with discussion), The Annals of Statistics, 22, 1701-1762.
36. Worledge, D. H., Stringham, R. S., and McClymont, A. S. (1982), "PWR Power Plant Reliability Data," Interim Report NP-2592, Electric Power Research Institute.