The MCMC Procedure



Aitkin, M., Anderson, D., Francis, B., and Hinde, J. (1989), Statistical Modelling in GLIM, Oxford: Oxford Science Publications.

Atkinson, A. C. (1979), “The Computer Generation of Poisson Random Variables,” Applied Statistics, 28, 29–35.

Atkinson, A. C. and Whittaker, J. (1976), “A Switching Algorithm for the Generation of Beta Random Variables with at Least One Parameter Less Than One,” Proceedings of the Royal Society of London, Series A, 139, 462–467.

Bacon, D. W. and Watts, D. G. (1971), “Estimating the Transition between Two Intersecting Straight Lines,” Biometrika, 58, 525–534.

Berger, J. O. (1985), Statistical Decision Theory and Bayesian Analysis, Second Edition, New York: Springer-Verlag.

Box, G. E. P. and Cox, D. R. (1964), “An Analysis of Transformations,” Journal of the Royal Statistics Society, Series B, 26, 211–234.

Carlin, B. P., Gelfand, A. E., and Smith, A. F. M. (1992), “Hierarchical Bayesian Analysis of Changepoint Problems,” Applied Statistics, 41(2), 389–405.

Chaloner, K. (1994), “Residual Analysis and Outliers in Bayesian Hierarchical Models,” in Aspects of Uncertainty: A Tribute to D. V. Lindley, 149–157, New York: Wiley.

Chaloner, K. and Brant, R. (1988), “A Bayesian Approach to Outlier Detection and Residual Analysis,” Biometrika, 75(4), 651–659.

Cheng, R. C. H. (1978), “Generating Beta Variates with Non-integral Shape Parameters,” Communications ACM, 28, 290–295.

Clayton, D. G. (1991), “A Monte Carlo Method for Bayesian Inference in Frailty Models,” Biometrics, 47, 467–485.

Congdon, P. (2003), Applied Bayesian Modeling, John Wiley & Sons.

Crowder, M. J. (1978), “Beta-Binomial Anova for Proportions,” Applied Statistics, 27, 34–37.

Draper, D. (1996), “Discussion of the Paper by Lee and Nelder,” Journal of the Royal Statistical Society, Series B, 58, 662–663.

Eilers, P. H. C. and Marx, B. D. (1996), “Flexible Smoothing with B-Splines and Penalties,” Statistical Science, 11, 89–121, with discussion.

Finney, D. J. (1947), “The Estimation from Individual Records of the Relationship between Dose and Quantal Response,” Biometrika, 34, 320–334.

Fisher, R. A. (1935), “The Fiducial Argument in Statistical Inference,” Annals of Eugenics, 6, 391–398.

Fishman, G. S. (1996), Monte Carlo: Concepts, Algorithms, and Applications, New York: John Wiley & Sons.

Gaver, D. P. and O’Muircheartaigh, I. G. (1987), “Robust Empirical Bayes Analysis of Event Rates,” Technometrics, 29, 1–15.

Gelfand, A. E., Hills, S. E., Racine-Poon, 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.

Gelman, A., Carlin, J., Stern, H., and Rubin, D. (2004), Bayesian Data Analysis, Second Edition, London: Chapman & Hall.

Gentleman, R. and Geyer, C. J. (1994), “Maximum Likelihood for Interval Censored Data: Consistency and Computation,” Biometrika, 81, 618–623.

Gilks, W. (2003), “Adaptive Metropolis Rejection Sampling (ARMS),” software from MRC Biostatistics Unit, Cambridge, UK,

Gilks, W. R. and Wild, P. (1992), “Adaptive Rejection Sampling for Gibbs Sampling,” Applied Statistics, 41, 337–348.

Holmes, C. C. and Held, L. (2006), “Bayesian Auxiliary Variable Models for Binary and Multinomial Regression,” Bayesian Analysis, 1(1), 145–168,

Ibrahim, J. G., Chen, M. H., and Sinha, D. (2001), Bayesian Survival Analysis, New York: Springer-Verlag.

Kass, R. E., Carlin, B. P., Gelman, A., and Neal, R. (1998), “Markov Chain Monte Carlo in Practice: A Roundtable Discussion,” The American Statistician, 52, 93–100.

Krall, J. M., Uthoff, V. A., and Harley, J. B. (1975), “A Step-up Procedure for Selecting Variables Associated with Survival,” Biometrics, 31, 49–57.

Kuhfeld, W. F. (2004), Conjoint Analysis, Technical report, SAS Institute Inc.,

Lin, D. Y. (1994), “Cox Regression Analysis of Multivariate Failure Time Data: The Marginal Approach,” Statistics in Medicine, 13, 2233–2247.

Matsumoto, M. and Kurita, Y. (1992), “Twisted GFSR Generators,” ACM Transactions on Modeling and Computer Simulation, 2(3), 179–194.

Matsumoto, M. and Kurita, Y. (1994), “Twisted GFSR Generators,” ACM Transactions on Modeling and Computer Simulation, 4(3), 254–266.

Matsumoto, M. and Nishimura, T. (1998), “Mersenne Twister: A 623-Dimensionally Equidistributed Uniform Pseudo-Random Number Generator,” ACM Transactions on Modeling and Computer Simulation, 8, 3–30.

McGrath, E. J. and Irving, D. C. (1973), Techniques for Efficient Monte Carlo Simulation, Volume II: Random Number Generation for Selected Probability Distributions, Technical report, Science Applications Inc., La Jolla, CA.

Michael, J. R., Schucany, W. R., and Haas, R. W. (1976), “Generating Random Variates Using Transformations with Multiple Roots,” American Statistician, 30(2), 88–90.

Pregibon, D. (1981), “Logistic Regression Diagnostics,” Annals of Statistics, 9, 705–724.

Ripley, B. D. (1987), Stochastic Simulation, New York: John Wiley & Sons.

Robert, C. (1995), “Simulation of Truncated Normal Variables,” Statistics and Computing, 5, 121–125.

Roberts, G. O., Gelman, A., and Gilks, W. R. (1997), “Weak Convergence and Optimal Scaling of Random Walk Metropolis Algorithms,” Annual of Applied Probability, 7, 110–120.

Roberts, G. O. and Rosenthal, J. S. (2001), “Optimal Scaling for Various Metropolis-Hastings Algorithms,” Statistical Science, 16, 351–367.

Rubin, D. B. (1981), “Estimation in Parallel Randomized Experiments,” Journal of Educational Statistics, 6, 377–411.

Schervish, M. J. (1995), Theory of Statistics, New York: Springer-Verlag.

Sharples, L. (1990), “Identification and Accommodation of Outliers in General Hierarchical Models,” Biometrika, 77, 445–453.

Spiegelhalter, D. J., Thomas, A., Best, N. G., and Gilks, W. R. (1996a), “BUGS Examples, Volume 1, Version 0.5, (version ii),” .

Spiegelhalter, D. J., Thomas, A., Best, N. G., and Gilks, W. R. (1996b), “BUGS Examples, Volume 2, Version 0.5, (version ii),” .