Identification of regeneration times in MCMC simulation, with application to adaptive schemes

Journal of Computational and Graphical Statistics

Volumn 14, Issue 2, 2005, Pages 436-458

  Brockwell, Anthony E ^a   Kadane, Joseph B ^a  

^a CARNEGIE MELLON UNIVERSITY   (United States)

Author keywords

Adaptive Markov chain Monte Carlo; Atoms; Burn in; Mixture approximations; Parallel processing; Regenerative simulation; Splitting

Indexed keywords

EID: 20744442841     PISSN: 10618600     EISSN: None     Source Type: Journal    
DOI: 10.1198/106186005X47453     Document Type: Article

References (32)

1. Carlin, B. P., and Gelfand, A. E. (1991), "An Iterative Monte Carlo Method for Nonconjugate Bayesian Analysis," Statistics and Computing, 1, 119-128.
2. Chauveau, D., and Vandekerkhove, P. (2002), "Improving Convergence of the Hastings-Metropolis Algorithm With an Adaptive Proposal," Scandinavian Journal of Statistics, 29, 13-29.
3. Chien, C., Goldsman, D., and Melamed, B. (1997), "Large-Sample Results for Batch Means," Management Science, 43, 1288-1295.
4. Crane, M. A., and Iglehart, D. L. (1975a), "Simulating Stable Stochasting Systems, I: General Multi-Server Queues," Journal of the Association of Computing Machinery, 21, 103-113.
5. _ (1975b), "Simulating Stable Stochasting Systems, II: Markov Chains," Journal of the Association of Computing Machinery, 21, 114-123.
6. Crane, M. A., and Lemoine, A. J. (1977), An Introduction to the Regenerative Method for Simulation Analysis, volume 4 of Lecture Notes in Control and Information Sciences, New York: Springer.
7. Gelfand, A. E., and Sahu, S. K. (1994), "On Markov Chain Monte Carlo Acceleration," Journal of Computational and Graphical Statistics, 3, 261-276.
8. Geyer, C. (1992), "Practical Markov Chain Monte Carlo," Statistical Science, 7, 473-483.
9. Geyer, C. J., and Thompson, E. A. (1995), "Annealing Markov Chain Monte Carlo with Applications to Ancestral Inference," Journal of the American Statistical Association, 90, 909-920.
10. Gilks, R., Roberts, G. O., and Sahu, S. K. (1998), "Adaptive Markov Chain Monte Carlo Through Regeneration," Journal of the American Statistical Association, 93, 1045-1054.
11. Gilks, W. R., Richardson, S., and Spiegelhalter, D. J. (1996), Markov Chain Monte Carlo in Practice, Boca Raton, FL: CRC Press.
12. Gilks, W. R., Roberts, G. O., and George, E. I. (1994), "Adaptive Direction Sampling," The Statistician, 43, 179-189.
13. Glynn, P. W., and Iglehart, D. L. (1990), "Simulation Output Analysis Using Standardized Time Series," Mathematics of Operations Research, 15, 1-16.
14. Hobert, J. P., Jones, G. L., Presnell, B., and Rosenthal, J. S. (2002), "On the Applicability of Regenerative Simulation in Markov Chain Monte Carlo," Biometrika, 89, 731-744.
15. Jones, G. L., and Hobert, J. P. (2001), "Honest Exploration of Intractable Probability Distributions via Markov Chain Monte Carlo," Statistical Science, 16, 312-334.
16. McLachlan, G., and Peel, D. (2000), Finite Mixture Models, New York: Wiley.
17. Meyn, S. P., and Tweedie, R. L. (1993), Markov Chains and Stochastic Stability, New York: Springer.
18. Møller, J., and Nicholls, G. K. (2005), "Perfect Simulation for Sample-Based Inference," Statistics and Computing, conditionally accepted.
19. Mykland, P., 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 Wahrscheinlichkeitstheorie und Vervandte Gebiete, 43, 309-318.
21. _ (1984), General Irreducible Markov Chains and Non-Negative Operators. Cambridge: Cambridge University Press.
22. Ratkowsky, D. A. (1983), Nonlinear Regression Modeling, New York: Dekker.
23. Revuz, D. (1975), Markov Chains, Amsterdam: North-Holland.
24. Ripley, B. D. (1987), Stochastic Simulation, New York: Wiley.
25. Robert, C. P. (1995), "Convergence Control Methods for Markov Chain Monte Carlo Algorithms," Statistical Science, 10, 230-253.
26. Robert, C. P., and Casella, G. (1999), Monte Carlo Statistical Methods, New York: Springer.
27. Roberts, G. O. (1996), "Markov Chain Concepts Related to Sampling Algorithms," in Markov Chain Monte Carlo in Practice, Boca Raton, FL: CRC Press, pp. 45-57.
28. Tierney, L. (1994), "Markov Chains for Exploring Posterior Distributions," The Annals of Statistics, 22, 1701-1728.
29. Tierney, L., and Mira, A. (1999), "Some Adaptive Monte Carlo Methods for Inference," Statistics in Medicine, 18, 2507-2515.
30. Titterington, D. M. (1984), "Recursive Parameter Estimation Using Incomplete Data," Journal of the Royal Statistical Society, Ser. B, 46, 257-267.
31. Ventura, V., Carta, R., Kass, R. E., Olson, C. R., and Gettner, S. N. (2002), "Statistical Analysis of Temporal Evolution in Single-Neuron Firing Rates," Biostatistics, 1, 1-20.
32. Warnes, G. (2000), The Normal Kernel Coupler: An Adaptive Markov Chain Monte Carlo Method for Efficiently Sampling from Multi-modal Distributions, PhD thesis, University of Washington.