Possible biases induced by MCMC convergence diagnostics

Journal of Statistical Computation and Simulation

Volumn 64, Issue 1, 1999, Pages 87-104

  Cowles, Mary Kathryn ^a   Roberts, Gareth O ^b   Rosenthal, Jeffrey S ^c  

^a UNIVERSITY OF IOWA   (United States)

^b LANCASTER UNIVERSITY   (United Kingdom)

^c UNIVERSITY OF TORONTO   (Canada)

Author keywords

Batch means; Bias; Convergence diagnostic; Estimation; Markov chain Monte Carlo

Indexed keywords

EID: 0033236319     PISSN: 00949655     EISSN: None     Source Type: Journal    
DOI: 10.1080/00949659908811968     Document Type: Article

References (27)

1. Best, N. G., Cowles, M. K. and Vines, K. (1995) CODA: Convergence diagnosis and output analysis software for Gibbs sampling output, Version 0.30. Tech. Rep., MRC Bio-statistics Unit, University of Cambridge.
2. Box, C. E. P. and Tiao, G. C. (1973) Bayesian inference in statistical analysis (Chapter 2). Addison-Wellesley, Reading, Massachusetts.
3. Brooks, S. P. and Roberts, G. O. (1996) Diagnosing convergence of Markov chain Monte Carlo algorithms. Preprint.
4. Cowles, M. K. and Carlin, B. P. (1996) Markov chain Monte Carlo convergence diagnostics: a comparative review. J. Amer. Stat. Assoc., 91, 883-904.
5. Cowles, M. K. and Rosenthal, J. S. (1998) A simulation approach to convergence rates for Markov chain Monte Carlo algorithms. Stat. and Comput., 8, 115-124.
6. Gelfand, A. E. and Smith, A. F. M. (1990) Sampling based approaches to calculating marginal densities. J. Amer. Stat. Assoc., 85, 398-409.
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 sampling. J. Amer. Stat. Soc., 85, 972-985.
8. Gelman, A. and Rubin, D. B. (1992) Inference from iterative simulation using multiple sequences. Stat. Sci., 7(4), 457-472.
9. Geman, S. and Geman, D. (1984) Stochastic relaxation, Gibbs distributions and the Bayesian restoration of images. IEEE Trans. on Pattern Analysis and Machine Intelligence, 6, 721-741.
10. Geweke, J. (1992) Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments. In: Bayesian Statistics, 4 (Bernardo, J. M. et al., Eds.), 169-193. Oxford University Press.
11. Geyer, C. (1992) Practical Markov chain Monte Carlo. Stat. Sci., 7(4), 473-483.
12. Hastings, W. K. (1970) Monte Carlo sampling methods using Markov chains and their applications. Biometrika, 57, 97-109.
13. Matthews, P. (1993) A slowly mixing Markov chain with implications for Gibbs sampling. Stat. Prob. Lett., 17, 231-236.
14. Metropolis, N., Rosenbluth, A., Rosenbluth, M., Teller, A. and Teller, E. (1953) Equations of state calculations by fast computing machines. J. Chem. Phys., 21, 1087-1091.
15. Meyn, S. P. and Tweedie, R. L. (1994) Computable bounds for convergence rates of Markov chains. Ann. Appl. Prob., 4, 981-1011.
16. Neal, R. M. (1993) Probabilistic inference using Markov chain Monte Carlo methods. Tech. Rep. CRG-TR-93-1, Dept. of Computer Science, University of Toronto.
17. Raftery, A. E. and Lewis, S. (1992) How many iterations in the Gibbs sampler? In: Bayesian Statistics, 4 (Bernardo, J. M. et al., Eds.), 763-773. Oxford University Press.
18. Roberts, G. O. (1992) Convergence diagnostics of the Gibbs sampler. In: Bayesian Statistics, 4, (Bernardo, J. M. et al., Eds.), 777-784. Oxford University Press.
19. 2 convergence of Markov chain Monte Carlo. In: Bayesian Statistics, and Econometrics: Essays in Honor of Arnold Zellner (Berry, D. et al., Eds.). North Holland, Amsterdam.
20. Rosenthal, J. S. (1995a) Rates of convergence of Gibbs sampling for variance components models. Ann. Stat., 23, 740-761.
21. Rosenthal, J. S. (1995b) Minorization conditions and convergence rates for Markov chain Monte Carlo. J. Amer. Stat. Assoc., 90, 558-566.
22. Rosenthal, J. S. (1995c) Convergence rates of Markov chains. SIAM Review, 37, 387-405.
23. Rosenthal, J. S. (1996) Analysis of the Gibbs sampler for a model related to James Stein estimators. Stat. and Comput., 6, 269-275.
24. Smith, A. F. M. and Roberts, G. O. (1993) Bayesian computation via the Gibbs sampler and related Markov chain Monte Carlo methods (with discussion). J. Roy. Stat. Soc. Ser. B, 55, 3-24.
25. Spiegelhalter, D. J., Thomas, A., Best, N. G. and Gilks, W. R. (1995) BUGS: Bayesian inference using Gibbs sampling. Version 0.30. Tech. Rep., MRC Biostatistics Unit, University of Cambridge.
26. Tanner, M. A. and Wong, W. H. (1987) The calculation of posterior distributions by data augmentation (with discussion). J. Amer. Stat. Assoc., 82, 528-550.
27. Wolfram, S. (1998) Mathematica: A system for doing mathematics by computer. Addison-Wesley, New York.