Self-regenerative Markov chain Monte Carlo with adaptation

Bernoulli

Volumn 9, Issue 3, 2003, Pages 395-422

  Sahu, Sujit K ^a   Zhigljavsky, Anatoly A ^b  

^a UNIVERSITY OF SOUTHAMPTON   (United Kingdom)

^b CARDIFF UNIVERSITY   (United Kingdom)

Author keywords

Adaptive method; Bayesian inference; Independence sampler; Metropolis Hastings algorithm; Regeneration

Indexed keywords

EID: 2442470429     PISSN: 13507265     EISSN: None     Source Type: Journal    
DOI: 10.3150/bj/1065444811     Document Type: Article

References (29)

1. Bates, D.M. and Watts, D.G. (1988) Nonlinear Regression Analysis and Its Applications. New York: Wiley.
2. Carlin, B.P. and Gelfand, A.E. (1991) An iterative Monte Carlo method for nonconjugate Bayesian analysis. Statist. Comput., 1, 119-128.
3. Chib, S. (1995) Marginal likelihood from the Gibbs output. J. Amer. Statist. Assoc., 90, 1313-1321.
4. Chib, S. and Greenberg, E. (1995) Understanding the Metropolis-Hastings algorithm. Amer. Statist., 49, 327-335.
5. Chib, S. and Jeliazkov, I. (2001) Marginal likelihood from the Metropolis-Hastings output. J. Amer. Statist. Assoc., 96, 270-281.
6. Gelfand, A.E. and Smith, A.F.M. (1990) Sampling based approaches to calculating marginal densities. J. Amer. Statist. Assoc., 85, 398-409.
7. Geyer, C.J. (1992) Practical Markov Chain Monte Carlo. Statist. Sci., 7, 473-483.
8. Gilks, W.R., Richardson, S. and Spiegelhalter, D.G. (1996) Markov Chain Monte Carlo in Practice. London: Chapman & Hall.
9. Gilks, W.R., Roberts, G.O. and Sahu, S.K. (1998) Adaptive Markov chain Monte Carlo through regeneration. J. Amer. Statist. Assoc., 93, 1045-1054.
10. Green, P.J. and Han, X.-L. (1992) Metropolis methods, Gaussian proposals, and antithetic variables. In P. Barone, A. Frigessi and M. Piccioni (eds), Stochastic Models, Statistical Methods, and Algorithms in Image Analysis, Lecture Notes in Statist. 74, pp. 142-164. Berlin: Springer-Verlag.
11. Hastings, W.K. (1970) Monte Carlo sampling methods using Markov chains and their applications. Biometrika, 57, 97-109.
12. Kass, R.E., Carlin, B.P., Gelman, A. and Neal, R. (1998) Markov chain Monte Carlo in practice: A roundtable discussion. Amer. Statist., 52, 93-100.
13. Liu, J.S. (1996) Metropolized independent sampling with comparisons to rejection sampling and importance sampling. Statist. Comput., 6, 113-119.
14. Mira, A. and Tierney, L. (2002) Efficiency and convergence properties of slice samplers. Scand. J. Statist., 29, 1-12.
15. Metropolis, N., Rosenbluth, A.W., Rosenbluth, M.N., Teller, A.H. and Teller, E. (1953) Equations of state calculations by fast computing machine. J. Chem. Phys., 21, 1087-1091.
16. Mykland, P. Tierney, L. and Yu, B. (1995) Regeneration in Markov chain samplers. J. Amer. Statist. Assoc., 90, 233-241.
17. Newton, M.A. and Raftery, A.E. (1994) Approximate Bayesian inference with the weighted likelihood bootstrap (with discussion). J. Roy. Statist. Soc. Ser. B, 56, 3-48.
18. Nummelin, E. (1984) General Irreducible Markov Chains and Non-Negative Operators. Cambridge: Cambridge University Press.
19. Peskun, P.H. (1973) Optimum Monte Carlo sampling using Markov chains. Biometrika, 60, 607-612.
20. Rao, C.R. (1973) Linear Statistical Inference and Its Applications. New York: Wiley.
21. Ratkowsky, D. (1983) Nonlinear Regression Modeling. New York: Marcel Dekker.
22. Ripley, B.D. (1987) Stochastic Simulation. New York: Wiley.
23. Robert, C.P. (1995) Convergence control methods for Markov chain Monte Carlo algorithms. Statist. Sci., 10, 231-253.
24. Robert, C.P. and Casella, G. (1999) Monte Carlo Statistical Methods. New York: Springer-Verlag.
25. Roberts, G.O. (1996) Markov chain concepts related to sampling algorithms. In W.R. Gilks, S. Richardson and D.J. Spiegelhalter (eds), Markov Chain Monte Carlo in Practice, pp. 45-57. London: Chapman & Hall.
26. Smith, A.F.M. and Roberts, G.O. (1993) Bayesian computation via the Gibbs sampler and related Markov chain Monte Carlo methods. J. Roy. Statist. Soc. Ser. B, 55, 3-23.
27. Smith, R.L. and Tierney, L. (1996) Exact transition probabilities for the independence Metropolis sampler. Technical Report, Department of Statistics, University of North Carolina, Chapel Hill.
28. Spiegelhalter, D.J., Thomas, A. and Best, N.G. (1996) Computation on Bayesian graphical models. In J.M. Bernardo, J.O. Berger, A.P. Dawid and A.F.M. Smith (eds), Bayesian Statistics 5, pp. 407-426. Oxford: Oxford University Press.
29. Tierney, L. (1994) Markov chains for exploring posterior distributions (with discussion). Ann. Statist., 22, 1701-1762.