Amit, Y. (1991), “On Rates of Convergence of Stochastic Relaxation for Gaussian and Non-Gaussian Distributions,” Journal of Multivariate Analysis, 38, 82–99.

Applegate, D. L., Kannan, R., and Polson, N. (1990), Random Polynomial Time Algorithms for Sampling from Joint Distributions, Technical report, Carnegie Mellon University, School of Computer Science.

Berger, J. O. (1985), Statistical Decision Theory and Bayesian Analysis, 2nd Edition, New York: Springer-Verlag.

Berger, J. O. (2006), “The Case for Objective Bayesian Analysis,” Bayesian Analysis, 3, 385–402, http://ba.stat.cmu.edu/journal/2006/vol01/issue03/berger.pdf.

Berger, J. O. and Wolpert, R. (1988), The Likelihood Principle, 2nd Edition, Hayward, CA: Institute of Mathematical Statistics.

Bernardo, J. M. and Smith, A. F. M. (1994), Bayesian Theory, New York: John Wiley & Sons.

Besag, J. (1974), “Spatial Interaction and the Statistical Analysis of Lattice Systems,” Journal of the Royal Statistical Society, Series B, 36, 192–326.

Billingsley, P. (1986), Probability and Measure, 2nd Edition, New York: John Wiley & Sons.

Box, G. E. P. and Tiao, G. C. (1973), Bayesian Inference in Statistical Analysis, New York: John Wiley & Sons.

Breiman, L. (1968), Probability, Reading, MA: Addison-Wesley.

Brooks, S. P. and Gelman, A. (1997), “General Methods for Monitoring Convergence of Iterative Simulations,” Journal of Computational and Graphical Statistics, 7, 434–455.

Brooks, S. P. and Roberts, G. O. (1998), “Assessing Convergence of Markov Chain Monte Carlo Algorithms,” Statistics and Computing, 8, 319–335.

Brooks, S. P. and Roberts, G. O. (1999), “On Quantile Estimation and Markov Chain Monte Carlo Convergence,” Biometrika, 86, 710–717.

Carlin, B. P. and Louis, T. A. (2000), Bayes and Empirical Bayes Methods for Data Analysis, 2nd Edition, London: Chapman & Hall.

Casella, G. and George, E. I. (1992), “Explaining the Gibbs Sampler,” American Statistician, 46, 167–174.

Chan, K. S. (1993), “Asymptotic Behavior of the Gibbs Sampler,” Journal of the American Statistical Association, 88, 320–326.

Chen, M.-H. and Shao, Q.-M. (1999), “Monte Carlo Estimation of Bayesian Credible and HPD Intervals,” Journal of Computational and Graphical Statistics, 8, 69–92.

Chen, M.-H., Shao, Q.-M., and Ibrahim, J. G. (2000), Monte Carlo Methods in Bayesian Computation, New York: Springer-Verlag.

Chib, S. and Greenberg, E. (1995), “Understanding the Metropolis-Hastings Algorithm,” American Statistician, 49, 327–335.

Congdon, P. (2001), Bayesian Statistical Modeling, Wiley Series in Probability and Statistics, Chichester, UK: John Wiley & Sons.

Congdon, P. (2003), Applied Bayesian Modeling, Wiley Series in Probability and Statistics, Chichester, UK: John Wiley & Sons.

Congdon, P. (2005), Bayesian Models for Categorical Data, Wiley Series in Probability and Statistics, Chichester, UK: John Wiley & Sons.

Cowles, M. K. and Carlin, B. P. (1996), “Markov Chain Monte Carlo Convergence Diagnostics: A Comparative Review,” Journal of the American Statistical Association, 91, 883–904.

DeGroot, M. H. and Schervish, M. J. (2002), Probability and Statistics, 3rd Edition, Reading, MA: Addison-Wesley.

Feller, W. (1968), An Introduction to Probability Theory and Its Applications, 3rd Edition, New York: John Wiley & Sons.

Gamerman, D. (1997), “Sampling from the Posterior Distribution in Generalized Linear Models,” Statistics and Computing, 7, 57–68.

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. B., Stern, H. S., and Rubin, D. B. (2004), Bayesian Data Analysis, 2nd Edition, London: Chapman & Hall.

Gelman, A. and Rubin, D. B. (1992), “Inference from Iterative Simulation Using Multiple Sequences,” Statistical Science, 7, 457–472.

Geman, S. and Geman, D. (1984), “Stochastic Relaxation, Gibbs Distribution, and the Bayesian Restoration of Images,” IEEE Transactions on Pattern Analysis and Machine Intelligence, 6, 721–741.

Geweke, J. (1992), “Evaluating the Accuracy of Sampling-Based Approaches to Calculating Posterior Moments,” in J. M. Bernardo, J. O. Berger, A. P. Dawid, and A. F. M. Smith, eds., Bayesian Statistics, volume 4, Oxford: Clarendon Press.

Gilks, W. R. (2003), “Adaptive Metropolis Rejection Sampling (ARMS),” software from MRC Biostatistics Unit, Cambridge, UK, http://www.maths.leeds.ac.uk/~wally.gilks/adaptive.rejection/web_page/Welcome.html.

Gilks, W. R., Best, N. G., and Tan, K. K. C. (1995), “Adaptive Rejection Metropolis Sampling within Gibbs Sampling,” Applied Statistics, 44, 455–472.

Gilks, W. R., Richardson, S., and Spiegelhalter, D. J. (1996), Markov Chain Monte Carlo in Practice, London: Chapman & Hall.

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

Goldstein, M. (2006), “Subjective Bayesian Analysis: Principles and Practice,” Bayesian Analysis, 3, 403–420, http://ba.stat.cmu.edu/journal/2006/vol01/issue03/goldstein.pdf.

Hastings, W. K. (1970), “Monte Carlo Sampling Methods Using Markov Chains and Their Applications,” Biometrika, 57, 97–109.

Heidelberger, P. and Welch, P. D. (1981), “A Spectral Method for Confidence Interval Generation and Run Length Control in Simulations,” Communications of the ACM, 24, 233–245.

Heidelberger, P. and Welch, P. D. (1983), “Simulation Run Length Control in the Presence of an Initial Transient,” Operations Research, 31, 1109–1144.

Jeffreys, H. (1961), Theory of Probability, 3rd Edition, Oxford: Oxford University Press.

Karlin, S. and Taylor, H. (1975), A First Course in Stochastic Processes, 2nd Edition, Orlando, FL: Academic Press.

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

Kass, R. E. and Wasserman, L. (1996), “Formal Rules of Selecting Prior Distributions: A Review and Annotated Bibliography,” Journal of the American Statistical Association, 91, 343–370.

Liu, C., Wong, W. H., and Kong, A. (1991a), Correlation Structure and Convergence Rate of the Gibbs Sampler (I): Application to the Comparison of Estimators and Augmentation Scheme, Technical report, University of Chicago, Department of Statistics.

Liu, C., Wong, W. H., and Kong, A. (1991b), Correlation Structure and Convergence Rate of the Gibbs Sampler (II): Applications to Various Scans, Technical report, University of Chicago, Department of Statistics.

Liu, J. S. (2001), Monte Carlo Strategies in Scientific Computing, New York: Springer-Verlag.

MacEachern, S. N. and Berliner, L. M. (1994), “Subsampling the Gibbs Sampler,” American Statistician, 48, 188–190.

McCullagh, P. and Nelder, J. A. (1989), Generalized Linear Models, 2nd Edition, London: Chapman & Hall.

Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N., Teller, A. H., and Teller, E. (1953), “Equation of State Calculations by Fast Computing Machines,” Journal of Chemical Physics, 21, 1087–1092.

Metropolis, N. and Ulam, S. (1949), “The Monte Carlo Method,” Journal of the American Statistical Association, 44, 335–341.

Meyn, S. P. and Tweedie, R. L. (1993), Markov Chains and Stochastic Stability, Berlin: Springer-Verlag.

Neal, R. M. (2003), “Slice Sampling,” Annals of Statistics, 31, 705–757.

Press, S. J. (2003), Subjective and Objective Bayesian Statistics, New York: John Wiley & Sons.

Raftery, A. E. and Lewis, S. M. (1992), “One Long Run with Diagnostics: Implementation Strategies for Markov Chain Monte Carlo,” Statistical Science, 7, 493–497.

Raftery, A. E. and Lewis, S. M. (1995), “The Number of Iterations, Convergence Diagnostics, and Generic Metropolis Algorithms,” in W. R. Gilks, D. J. Spiegelhalter, and S. Richardson, eds., Markov Chain Monte Carlo in Practice, London: Chapman & Hall.

Robert, C. P. (2001), The Bayesian Choice, 2nd Edition, New York: Springer-Verlag.

Robert, C. P. and Casella, G. (2004), Monte Carlo Statistical Methods, 2nd Edition, New York: Springer-Verlag.

Roberts, G. O. (1996), “Markov Chain Concepts Related to Sampling Algorithms,” in W. R. Gilks, D. J. Spiegelhalter, and S. Richardson, eds., Markov Chain Monte Carlo in Practice, 45–58, London: Chapman & Hall.

Rosenthal, J. S. (1991a), Rates of Convergence for Data Augmentation on Finite Sample Spaces, Technical report, Harvard University, Department of Mathematics.

Rosenthal, J. S. (1991b), Rates of Convergence for Gibbs Sampling for Variance Component Models, Technical report, Harvard University, Department of Mathematics.

Ross, S. M. (1997), Simulation, 2nd Edition, Orlando, FL: Academic Press.

Schervish, M. J. and Carlin, B. P. (1992), “On the Convergence of Successive Substitution Sampling,” Journal of Computational and Graphical Statistics, 1, 111–127.

Spiegelhalter, D. J., Best, N. G., Carlin, B. P., and Van der Linde, A. (2002), “Bayesian Measures of Model Complexity and Fit,” Journal of the Royal Statistical Society, Series B, 64(4), 583–616, with discussion.

Tanner, M. A. (1993), Tools for Statistical Inference: Methods for the Exploration of Posterior Distributions and Likelihood Functions, New York: Springer-Verlag.

Tanner, M. A. and Wong, W. H. (1987), “The Calculation of Posterior Distributions by Data Augmentation,” Journal of the American Statistical Association, 82, 528–540.

Tierney, L. (1994), “Markov Chains for Exploring Posterior Distributions,” Annals of Statistics, 22, 1701–1762.

von Mises, R. (1918), “Über die 'Ganzzahligkeit' der Atomgewicht und verwandte Fragen,” Physikalische Zeitschrift, 19, 490–500.

Wasserman, L. (2004), All of Statistics: A Concise Course in Statistical Inference, New York: Springer-Verlag.