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Theory and Method

Gibbs Sampler Convergence Criteria

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Pages 921-927 | Received 01 Sep 1992, Published online: 27 Feb 2012

References

  • Albert , J. H. and Chib , S. 1993 . “Bayesian Analysis of Binary and Polychotomous Response Data,” . Journal of the American Statistical Association , 88 : 669 – 679 .
  • Anderson , T. W. 1971 . The Statistical Analysis of Time Series , New York : John Wiley .
  • Bartlett , M. S. 1946 . “On the Theoretical Specification and Sampling Properties of Autocorrelated Time Series,” . Journal of the Royal Statistical Society , VIII : 25 – 41 . (Supplement)
  • Casella , G. and George , E. I. 1992 . “Explaining the Gibbs Sampler,” . The American Statistician , 46 : 167 – 174 .
  • Chib , S. 1991 . “Bayes Regression With Autocorrelated Errors: A Gibbs Sampling Approach,” . Journal of Econometrics , 58 : 275 – 294 .
  • Gelfand , A. E. , Hills , S. E. , RacinePoon , A. and Smith , A. F. M. 1990 . “Illustration of Bayesian Inference in Normal Data Models Using Gibbs Sampling,” . Journal of the American Statistical Association , 85 : 972 – 985 .
  • 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 .
  • Gelman , A. and Rubin , D. B. 1992 . “Inference from Iterative Simulation Using Multiple Sequences” . Statistical Science , 7 : 457 – 472 . (with discussion)
  • Geman , S. and Geman , D. 1984 . “Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images,” . IEEE Transactions on Pattern Analysis and Machine Intelligence , PAMI-6 : 721 – 741 .
  • Geweke , J. 1992 . “Evaluating the Accuracy of Sampling-Based Approaches to the Calculation of Posterior Moments” . In Bayesian Statistics 4 , Edited by: Bernardo , J. M. , Berger , J. O. , Dawid , A. P. and Smith , A. F.M. 169 – 193 . New York : Oxford University Press . (with discussion)
  • Jeffreys , H. 1967 . Theory of Probability, , 3rd ed. , London : Oxford University Press .
  • McCulloch , R. and Rossi , P. E. 1991 . “An Exact Likelihood Analysis of the Multinomial Probit Model,” . Journal of Econometrics , 64 : 207 – 240 .
  • Min , C. 1992 . “Unconditional Estimation of Time-Varying-Parameter Models: A Gibbs Sampling Approach,” , H. G. B. Alexander Research Foundation, Graduate School of Business . unpublished manuscript, University of Chicago
  • Poirier , D. J. 1991 . “Bayesian Empirical Studies in Economics and Finance,” . Journal of Econometrics (Annals Issue) , : 49
  • Racine-Poon , A. 1992 . Comment on “Inference from Iterative Simulation Using Multiple Sequences,” . Statistical Science , 7 : 492 – 493 . by A. Gelman and D. B. Rubin
  • Ritter , C. and Tanner , M. A. 1992 . “Facilitating the Gibbs Sampler: The Gibbs Stopper and the Griddy-Gibbs Sampler,” . Journal of the American Statistical Association , 87 : 861 – 868 .
  • Roberts , G. O. “Convergence Diagnostics for the Gibbs Sampler,” . paper presented at the Fourth Valencia International Meeting on Bayesian Statistics . April 1991 .
  • Roberts , G. O. 1992 . “Convergence Diagnostics of the Gibbs Sampler,” . In Bayesian Statistics 4 , Edited by: Bernardo , J. M. , Berger , J. O. , Dawid , A. P. and Smith , A. F.M. 775 – 782 . New York : Oxford University Press .
  • Tanner , M. A. 1991 . Tools for Statistical Inference: Observed Data and Data Augmentation Methods , New York : Springer-Verlag .
  • Zellner , A. 1961 . “Econometric Estimation With Temporally Dependent Disturbance Terms,” . International Economic Review, 2 , : 164 – 178 .
  • Zellner , A. 1971 . An Introduction to Bayesian Inference in Econometrics , New York : John Wiley . reprinted by Krieger Publishing, 1987
  • Zellner , A. , Bauwens , L. and vanDijk , H. K. 1988 . “Bayesian Specification Analysis and Estimation of Simultaneous Equation Models Using Monte Carlo Methods,” . Journal of Econometrics , 38 : 39 – 72 .
  • Zellner , A. and Min , C. 1993 . “Bayesian Analysis, Model Selection and Prediction,” . In Physics and Probability: Essays in Honor of Edwin T. Jaynes , Edited by: Grandy , W. T. and Milonni , P. W. 195 – 206 . Cambridge , , UK : Cambridge University Press .
  • Zurbenko , I. G. 1991 . “Spectral Analysis of Non-Stationary Time Series,” . International Statistical Review , 59 : 163 – 173 .

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