Discretization of continuous markov chains and markov chain monte carlo convergence assessment

Journal of the American Statistical Association

Volumn 93, Issue 443, 1998, Pages 1055-1067

  Guihenneuc jouyaux, Chantal ^a   Robert, Christian P ^b  

^a CNRS   (France)

^b CREST   (France)

Author keywords

Divergence; Ergodic theorem; Finite state space; Markov chain Monte Carlo algorithm; Multiple chains; Renewal theory; Renewal time; Stopping time

Indexed keywords

EID: 85012534904     PISSN: 01621459     EISSN: 1537274X     Source Type: Journal    
DOI: 10.1080/01621459.1998.10473767     Document Type: Article

References (23)

1. Asmussen, S. (1979), Applied Probability and Queues, New York: Wiley.
2. Battacharya, R. N., and Waymire, E. C. (1990), Stochastic Processes With Applications, New York: Wiley.
3. Chauveau, D., and Diebolt, J. (1997), "MCMC Convergence Diagnostic via the Central Limit Theorem," technical report. Université de Marne-la-Vallee.
4. Diebolt, J., and Robert, C. P. (1993), "The Duality Principle," Journal of the Royal Statistical Society, Ser. B, 55, 71-72.
5. Diebolt, J., and Robert, C. P. (1994), "Estimation of Finite Mixture Distributions Through Bayesian Sampling," Journal of the Royal Statistical Society, Ser. B, 56, 163-175.
6. Feller, W. (1970), An Introduction to Probability Theory and Its Applications, Vol. 1, New York: Wiley.
7. Gaver, D. P., and O'Muircheartaigh, I. G. (1987), "Robust Empirical Bayes Analysis of Event Rates," Technometrics 29, 1-15.
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. Geyer, C. J. (1992), "Practical Monte Carlo Markov Chain" (with discussion). Statistical Science, 7, 473-511.
10. Gilks, W. R., Roberts, G. O., and Sahu, S. K. (1997), "Adaptive Markov Chain Monte Carlo Through Regeneration," technical report, Cambridge University, MRC Biostatistics Unit.
11. 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.
12. Kemeny, J. G., and Snell, S. L. (1960), Finite Markov Chains, Princeton, NJ: Van Nostrand.
13. Meyn, S. P., and Tweedie, R. L. (1993), Markov Chains and Stochastic Stability, London: Springer-Verlag.
14. Mykland, P., Tierney, L., and Yu, B. (1995), "Regeneration in Markov Chain Samplers," Journal of the American Statistical Association, 90, 233-241.
15. O Ruanaidh, J. J. K., and Fitzgerald, W. J. (1996), Numerical Bayesian Methods Applied to Signal Processing, New York: Springer-Verlag.
16. Propp, J. G., and Wilson, D. B. (1995), "Exact Sampling With Coupled Markov Chains and Applications to Statistical Mechanics," technical report, Massachussetts Institute of Technology, Dept, of Mathematics.
17. Raftery, A., and Lewis, S. (1992), "How Many Iterations in the Gibbs Sampler?" in Bayesian Statistics 4, eds. J. M. Bernardo, J. O. Berger, A. P. Dawid, and A. F. M. Smith, Oxford, UK: Oxford University Press, pp. 765-776.
18. Raftery, A. E. and Lewis, S. (1996), "Implementing MCMC" in Markov chain Monte-Carlo in Practice, eds. W. R. Gilks, S. T. Richardson, and D. J. Spiegelhalter, London: Chapman and Hall, pp. 115-130.
19. Robert, C. R (1995), "Convergence Control Techniques for Monte Carlo Markov Chain Algorithms," Statistical Science, 10, 231-253.
20. Robert, C. P. (1996), Methodes de Monte Carlo par Chai nes de Markov, Paris: Economica.
21. Roberts, G. O., and Tweedie, R. L. (1996), "Geometric Convergence and Central Limit Theorems for Multidimensional Hastings and Metropolis Algorithms, Biometrika, 83, 95-110.
22. Tanner, M. (1991), Tools for Statistical Inference: Observed Data and Data Augmentation Methods, Lecture Notes in Statistics 67, New York: Springer-Verlag.
23. Yu, B., and Mykland, P. (1994), "Looking at Markov Samplers Through Cusum Path Plots: A Simple Diagnostic Idea," Technical Report 413, University of California-Berkeley, Dept, of Statistics.