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, School of Computer Science, Carnegie Mellon University.
Berger, J. O. (1985). Statistical Decision Theory and Bayesian Analysis. 2nd ed. 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 ed. 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 ed. 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 ed. 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. Chichester, UK: John Wiley & Sons.
Congdon, P. (2003). Applied Bayesian Modeling. Chichester, UK: John Wiley & Sons.
Congdon, P. (2005). Bayesian Models for Categorical Data. 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 ed. Reading, MA: Addison-Wesley.
Feller, W. (1968). An Introduction to Probability Theory and Its Applications. 3rd ed. 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 ed. 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 Bayesian Statistics, vol. 4, edited by J. M. Bernardo, J. O. Berger, A. P. Dawid, and A. F. M. Smith, 169–193. 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.” Journal of the Royal Statistical Society, Series C 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.” Journal of the Royal Statistical Society, Series C 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.
Hoffman, M. D., and Gelman, A. (2014). “The No-U-Turn Sampler: Adaptively Setting Path Lengths in Hamiltonian Monte Carlo.” Journal of Machine Learning Research 15:1351–1381.
Jeffreys, H. (1961). Theory of Probability. 3rd ed. Oxford: Oxford University Press.
Karlin, S., and Taylor, H. (1975). A First Course in Stochastic Processes. 2nd ed. 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, Department of Statistics, University of Chicago.
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, Department of Statistics, University of Chicago.
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 ed. 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.
Neal, R. M. (2011). “MCMC Using Hamiltonian Dynamics.” In Handbook of Markov Chain Monte Carlo, edited by S. Brooks, A. Gelman, G. L. Jones, and X.-L. Meng, 113–161. Boca Raton, FL: CRC Press.
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 Markov Chain Monte Carlo in Practice, edited by W. R. Gilks, D. J. Spiegelhalter, and S. Richardson, 115–130. London: Chapman & Hall.
Robert, C. P. (2001). The Bayesian Choice. 2nd ed. New York: Springer-Verlag.
Robert, C. P., and Casella, G. (2004). Monte Carlo Statistical Methods. 2nd ed. New York: Springer-Verlag.
Roberts, G. O. (1996). “Markov Chain Concepts Related to Sampling Algorithms.” In Markov Chain Monte Carlo in Practice, edited by W. R. Gilks, D. J. Spiegelhalter, and S. Richardson, 45–58. London: Chapman & Hall.
Rosenthal, J. S. (1991a). Rates of Convergence for Data Augmentation on Finite Sample Spaces. Technical report, Department of Mathematics, Harvard University.
Rosenthal, J. S. (1991b). Rates of Convergence for Gibbs Sampling for Variance Component Models. Technical report, Department of Mathematics, Harvard University.
Ross, S. M. (1997). Simulation. 2nd ed. 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 64:583–616. 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.