Note on the Sampling Distribution for the Metropolis-Hastings Algorithm

References

• Bernardo , J. M. and Smith , A. F. M. 1994 . Bayesian Theory John Wiley & Sons .
   Google Scholar
• Besag , J. , Green , P. , Higdon , D. and Mengersen , K. 1995 . Bayesian computation and stochastic systems . Statistical Science , 10 ( 1 ) : 3 – 66 . (with discussion)
   Web of Science ®Google Scholar
• Carlin , B. P. and Louis , T. A. 1996 . Bayes and Empirical Bayes Methods for Data Analysis Chapman & Hall .
   Google Scholar
• Chen , M. H. , Shao , Q. M. and Ibrahim , J. G. 2000 . Monte Carlo Methods in Bayesian Computation Springer-Verlag .
   Google Scholar
• Chib , S. and Greenberg , E. 1995 . Understanding the Metropolis-Hastings algorithm . The American Statistician , 49 ( 4 ) : 327 – 335 .
   Web of Science ®Google Scholar
• Chib , S. , Greenberg , E. and Winkelmann , R. 1998 . Posterior simulation and Bayes factors in panel count data models . Journal of Econometrics , 86 ( 1 ) : 33 – 54 .
   Google Scholar
• Gamerman , D. 1997 . Markov Chain Monte Carlo: Stochastic Simulation for Bayesian Inference Chapman & Hall .
   Google Scholar
• Gelman , A. , Roberts , G. O. and Gilks , W. R. 1995 . “ Efficient metropolis jumping rules ” . In Bayesian Statistics Edited by: Bernardo , J. M. , Berger , J. O. , Dawid , A. P. and Smith , A. F. M. Vol. 5 , pp. 599 – 607 . Oxford University Press .
   Google Scholar
• Geweke , J. 1992 . “ Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments ” . In Bayesian Statistics Edited by: Bernardo , J. M. , Berger , J. O. , Dawid , A. P. and Smith , A. F. M. Vol. 4 , 169 – 193 . Oxford University Press . (with discussion)
   Google Scholar
• Geweke , J. 1996 . “ Monte Carlo simulation and numerical integration ” . In Handbook of Computational Economics Edited by: Amman , H. M. , Kendrick , D. A. and Rust , J. Vol. 1 , pp. 731 – 800 . North-Holland
   Google Scholar
• Geweke , J. and Tanizaki , H. 1999 . On Markov Chain Monte-Carlo methods for nonlinear and non-Gaussian state-space models . Communications in statistics, Simulation and Computation , 28 ( 4 ) : 867 – 894 .
   Web of Science ®Google Scholar
• Geweke , J. and Tanizaki , H. 2001 . Bayesian estimation of state-space model using the Metropolis-Hastings algorithm within Gibbs sampling . Computational Statistics and Data Analysis , 37 ( 2 ) : 151 – 170 .
   Web of Science ®Google Scholar
• Mengersen , K. L. , Robert , C. P. and Guihenneuc-Jouyaux , C. 1999 . “ MCMC convergence diagnostics: a review ” . In Bayesian Statistics Edited by: Bernardo , J. M. , Berger , J. O. , Dawid , A. P. and Smith , A. F. M. Vol. 6 , 514 – 440 . Oxford University Press . (with discussion)
   Google Scholar
• Mengersen , K. L. and Tweedie , R. L. 1996 . Rates of convergence of the Hastings and Metropolis algorithms . Annals of Statistics , 24 ( 1 ) : 101 – 201 .
   Web of Science ®Google Scholar
• O'Hagan , A. 1994 . Kendall's Advanced Theory of Statistics Vol. 2B , Edward Arnold . (Bayesian Inference)
   Google Scholar
• Robert , C. P. and Casella , G. 1999 . Monte Carlo Statistical Methods Springer-Verlag .
   Google Scholar
• Roberts , G. O. and Smith , A. F. M. 1994 . Simple conditions for the convergence of the Gibbs sampler and Metropolis-Hastings algorithms . Stochastic Processes and Their Applications , 49 ( 2 ) : 207 – 216 .
   Web of Science ®Google Scholar
• Smith , A. F. M. and Roberts , G. O. 1993 . Bayesian computation via Gibbs sampler and related Markov chain Monte Carlo methods . Journal of the Royal Statistical Society, Ser. B , 55 ( 1 ) : 3 – 23 .
   Google Scholar
• Tierney , L. 1994 . Markov Chains for exploring posterior distributions . The Annals of Statistics , 22 ( 4 ) : 1701 – 1762 .
   Web of Science ®Google Scholar