References
- Arnold , B. C. , Castillo , E. , Sarabia , J. M. ( 1999 ), Conditional Specification of Statistical Models . New York : Springer .
- Arnold , B. C. , Press , S. ( 1989 ). Compatible conditional distributions . Journal of the American Statistical Association 84 : 152 – 156 .
- Barndorff-Nielsen , O. E. ( 1978 ). Information and Exponential Families in Statistical Theory . New York : John Wiley .
- Bishop , Y. , Fienberg , S. E. , Holland , P. W. ( 1975 ), Discrete Multivariate Analysis . Cambridge , MA : M.I.T. Press .
- Casella , G. , George , E. I. ( 1992 ). Explaining the Gibbs Sampler . The American Statistician 46 : 167 – 174 .
- Chen , S. H. , Ip , E. H. , Wang , Y. J. ( 2011 ), Gibbs Ensembles for nearly compatible and incompatible conditional models . Journal of Computational Statistic and Data Analysis 55 : 1760 – 1769 .
- Diaconis , P. , Stroock , D. (1991). Geometric bounds for eigenvalues of Markov chains. Annals of Applied Probability 1:36–61.
- Flegal , J. M. , Haran , M. , Jones , G. L. ( 2008 ). Markov Chain Monte Carlo: Can we trust the third significant figure? Statistical Science 23 : 250 – 260 .
- Gelfand , A. E. ( 2002 ). Gibbs Sampling . In: Raftery , A. E. , Tanner , M. A. , Wells , M. T. , eds. Statistics in the 21th Century . Boca Raton , FL : Chapman and Hall/CRC , pp. 341 – 349 .
- Gelman , A. , Rubin , D. B. ( 1992 ). Inference from iterative simulation using multiple sequences (with discussions) . Statistical Science 7 : 457 – 472 .
- Ip , E. H. , Wang , Y. J. ( 2009 ). Canonical representation of conditionally specified multivariate discrete distributions . Journal of Multivariate Analysis 100 : 1281 – 1290 .
- Koehler , E. , Brown , E. , Haneuse , S.J.-P.A. ( 2009 ). On the assessment of monte carlo error in simulation-based statistical analysis . The American Statistician 63 : 155 – 162 .
- Liu , J. S. ( 1996 ). Discussions on “statistical theory and Monte Carlo algorithms (with discussions)” . TEST 5 : 305 – 310 .
- Ng , K. W. ( 1997 ). Inversion of Bayes formula: explicit formulas for unconditional Pdf . In: Johnson , N. L. , Balakrishnan , N. , eds. Advances in the Theory and Practice in Statistics—A Volume in Honor of Samuel Kotz . New York : Wiley pp. 571 – 584 .
- Tan , M. , Tian , G. L. , Ng , K. W. ( 2010 ). Bayesian Missing Data Problems: EM, Data Augmentation and Non-iterative Computations . Boca Raton , FL : Chapman and Hall/CRC .
- Robert , C. P. , Casella , G. ( 2004 ). Monte Carlo Statistical Methods . New York : Springer .
- Tian , G. L. , Tan , M. ( 2003 ). Exact statistical solution using the inverse Bayesian formula . Statistics and Probability Letter 62 : 305 – 315 .
- Tian , G. L. , Tan , M. , Ng , K. W. ( 2009 ). A unified method for checking compatibility and uniqueness for finite discrete conditional distributions . Communications in Statistics: Theory and Methods 38 : 115 – 129 .
- Wang , Y. J. ( 1987 ). Probability integral for bivariate normal distributions: A contingency-table approach . Biometrika 74 : 185 – 190 .
- Wang , Y. J. ( 1997 ). Multivariate normal integrals and contingency tables with ordered categories . Psychometrika 62 : 267 – 284 .