Journal of the Royal Statistical Society: Series B (Methodological)Volume 55, Issue 1 p. 53-102 DiscussionFree Access Discussion on the Meeting on the Gibbs Sampler and Other Markov Chain Monte Carlo Methods First published: September 1993 https://doi.org/10.1111/j.2517-6161.1993.tb01469.xCitations: 2AboutPDF ToolsExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat REFERENCES IN THE DISCUSSION Adler, S. L. (1981) Over-relaxation method for the Monte Carlo evaluation of the partition function for multiquadratic actions. Phys. Rev. D, 23, 2901– 2904. Agresti, A. (1990) Categorical Data Analysis. New York: Wiley. Aitchison, J. (1986) The Statistical Analysis of Compositional Data. London: Chapman and Hall. Allen, M. P. and Tildesley, D. J. (1987) Computer Simulation of Liquids. Oxford: Clarendon. Amit, Y. (1991) On rates of convergence of stochastic relaxation for Gaussian and non-Gaussian distributions. J. Multiv. Anal., 38, 82– 99. Amit, Y. and Grenander, U. (1991) Comparing sweep strategies for stochastic relaxation. J. Multiv. Anal., 37, 197– 222. Applegate, D., Kannan, R. and Polson, N. G. (1990) Random polynomial time algorithms for sampling from joint distributions. Arslan, O., Constable, P. D. L. C. and Kent, J. T. (1992) Domains of convergence of the EM algorithm. Research Report STAT 92/08. University of Leeds, Leeds. Aykroyd, R. G. (1992) A Bayesian partition model for the analysis of autoradiographic images. Reports on Statistics and Operational Research, SOR 92-46. Department of Mathematics, University of Bradford, Bradford. Aykroyd, R. G. and Green, P. J. (1991) Global and local priors, and the location of lesions using gamma-camera imagery. Phil. Trans. R. Soc. Lond. A, 337, 323– 342. Azzalini, A. and Bowman, A. W. (1990) A look at some data on the Old Faithful Geyser. Appl. Statist., 39, 357– 365. Barone, P. and Frigessi, A. (1989) Improving stochastic relaxation for Gaussian random fields. Probab. Engng Inform. Sci., 4, 369– 389. Batrouni, G. G., Katz, G. R., Kronfeld, A. S., Lepage, G. P., Svetitsky, B. and Wilson, K. G. (1985) Langevin simulations of lattice field theories. Phys. Rev. D, 32, 2736– 2747. Bennett, A. and Craw, I. (1991) Finding image features using deformable templates and detailed prior statistical knowledge. In Proc. British Machine Vision Conf. (ed. P. Mowforth), pp. 232– 239. New York: Springer. Benson, P. J. and Perrett, D. I. (1991) Perception and recognition of photographic quality facial caricatures: implications for the recognition of natural images. Eur. J. Cogn. Psychol., 3, 105– 135. Berg, B. A. and Neuhaus, T. (1991) Multicanonical algorithms for first order phase transitions. Phys. Lett. B, 267, 249– 253. Bernardo, J. M. (1979) Reference posterior distributions for Bayesian inference. J. R. Statist. Soc. B, 41, 113– 128. Berretti, A. and Sokal, A. D. (1985) New Monte Carlo method for the self-avoiding walk. J. Statist. Phys., 40, 483– 531. Berzuini, C. and Larizza, C. (1992) Using serial measurements of immunological/viral indicators to predict therapy outcome in patients with post-transplant infection. Report RIDIS 66/92. Dipartimento di Informatica e Sistemistica dell' Università di Pavia, Pavia. Besag, J. (1974) Spatial interaction and the statistical analysis of lattice systems (with discussion). J. R. Statist. Soc. B, 36, 192– 236. Besag, J. (1986) On the statistical analysis of dirty pictures (with discussion). J. R. Statist. Soc. B, 48, 259– 302. Besag, J. and Clifford, P. (1989) Generalized Monte Carlo significance tests. Biometrika, 76, 633– 642. Besag, J. and Clifford, P. (1991) Sequential Monte Carlo p-values. Biometrika, 78, 301– 304. Besag, J. E., York, J. C. and Mollié, A. (1991) Bayesian image restoration, with two applications in spatial statistics (with discussion). Ann. Inst. Statist. Math., 43, 1– 59. Bookstein, F. L. (1989) Principal Warps; thin-plate splines and the decomposition of deformations. IEEE Trans. Pattn Anal. Mach. Intell., 11, 567– 585. Bresnahan, T. F. (1981) Departures from marginal-cost pricing in American automobile industry, estimates from 1977-1978. J. Econometr., 17, 201– 227. Brewer, M. J., Aitken, C. G. G., Luo, Z. and Gammerman, A. (1992) Stochastic simulation in mixed graphical association models. In Proc. COMPSTAT 1992, pp. 257– 262. Buck, C. E., Litton, C. D. and Smith, A. F. M. (1992) Calibration of radiocarbon results pertaining to related archaeological events. J. Archaeol. Sci., 19, 497– 512. Buck, C. E., Litton, C. D. and Stephens, D. A. (1993) Detecting a change in the shape of a prehistoric corbelled tomb. Statistician, 42, in the press. Burridge, J. (1981) Empirical Bayes analysis of survival time data. J. R. Statist. Soc. B, 43, 65– 75. Caracciolo, S., Edwards, R. G., Pelissetto, A. and Sokal, A. D. (1992) Wolff-type embedding algorithms for general nonlinear σ-models. Submitted to Nucl. Phys. B. Caracciolo, S., Pelissetto, A. and Sokal, A. D. (1991) Nonlocal Monte Carlo algorithm for self-avoiding walks with fixed endpoints. J. Statist. Phys., 60, 1– 53. Cassandro, M., Galves, A. and Picco, P. (1991) Dynamical phase transition in disordered systems: the study of a random walk model. Ann. Inst. H. Poincare, 55, 689– 705. Celeux, G. and Diebolt, J. (1985) The SEM algorithm: A probabilistic teacher algorithm derived from the EM algorithm for the mixture problem. Comput. Statist. Q., 2, 73– 82. Celeux, G. and Diebolt, J. (1987) A probabilistic teacher algorithm for iterative maximum likelihood estimation. In Classification and Related Methods of Data Analysis (ed. H. H. Bock), pp. 617– 623. Amsterdam: North-Holland. Chen, S., Doolen, G. D. and Matthaeus, W. H. (1991) Lattice gas automata for simple and complex fluids. J. Statist. Phys., 64, 1133– 1162. Clayton, D. G. (1991) A Monte Carlo method for Bayesian inference in frailty models. Biometrics, 47, 467– 485. Cleveland, W. S. and Devlin, S. J. (1988) Locally weighted regression: An approach to regression analysis by local fitting. J. Am. Statist. Ass., 83, 596– 610. Clifford, P. and Middleton, R. D. (1989) Reconstruction of polygonal images. J. Appl. Statist., 16, 409– 422. Craw, I. and Cameron, P. (1991) Parameterizing images for recognition and reconstruction. In Proc. British Machine Vision Conf. (ed. P. Mowforth), pp. 367– 370. New York: Springer. Creutz, M. (1979) Confinement and the critical dimensionality of space-time. Phys. Rev. Lett., 43, 553– 556. Darcy, H. (1856) Les Fontaines Publiques de la Ville de Dijon. Paris: Malmont. Darroch, J. N., Lauritzen, S. L. and Speed, T. P. (1980) Markov fields and log linear models for contingency tables. Ann. Statist., 8, 522– 539. Dempster, A. P. (1971) Covariance selection. Biometrics, 27, 157– 171. Dempster, A. P., Selwyn, M. R. and Weeks, B. J. (1983) Combining historical and randomized controls for assessing trends in proportions. J. Am. Statist. Ass., 78, 221– 227. Diaconis, P. (1988) Group representations in probability and statistics. IMS Lect. Ser., 11. Diaconis, P. and Hanlon, P. (1992) Eigen analysis for some examples of the Metropolis algorithm. Technical Report. Department of Mathematics, Harvard University, Cambridge. Diaconis, P. and Saloff-Coste, L. (1992) Comparison theorems for reversible Markov chains. Technical Report. Department of Mathematics, Harvard University, Cambridge. Diaconis, P. and Stroock, D. (1991) Geometric bounds for eigenvalues of Markov chains. Ann. Appl. Probab., 1, 36– 61. Diebolt, J. and Robert, C. P. (1992) Estimation of finite mixture distributions through Bayesian sampling. Submitted to J. R. Statist. Soc. B. Diggle, P. J. (1976) A spatial stochastic model of inter-plant competition. J. Appl. Probab., 13, 662– 671. Draper, D., Hodges, J. S., Mallows, C. L. and Pregibon, D. (1993) Exchangeability and data analysis (with discussion). J. R. Statist. Soc. A, 156, 9– 37. Edwards, R. G., Ferreira, S. J., Goodman, J. and Sokal, A. D. (1992) Multi-grid Monte Carlo: III, Two-dimensional O(4)-symmetric nonlinear σ-model. Nucl. Phys. B, to be published. Edwards, R. G., Goodman, J. and Sokal, A. D. (1991) Multi-grid Monte Carlo: II, Two-dimensional XY model. Nucl. Phys. B, 354, 289– 327. Ford, E. D. (1975) Competition and stand structure in some even-aged plant monocultures. J. Ecol., 63, 311– 333. Frigessi, A. and den Hollander, F. (1992) A dynamical phase transition in a caricature of a spin glass. to be published. Frigessi, A., Hwang, C.-R. and Younes, L. (1992) Optimal spectral structure of reversible stochastic matrices, Monte Carlo methods and the simulation of Markov random fields. Ann. Appl. Probab., 2, 610– 628. Gail, M. H., Santner, T. J. and Brown, C. C. (1980) An analysis of comparative carcinogenesis experiments with multiple times to tumor. Biometrics, 36, 255– 266. Gelfand, A. E. and Carlin, B. P. (1991) Maximum likelihood estimation for constrained or missing data model. Research Report 91-002. Division of Biostatistics, University of Minnesota, Minneapolis. Gelfand, A. E., Dey, D. K. and Chang, H. (1992) Model determination using predictive distributions, with implementation via sampling-based methods. In Bayesian Statistics 4 (eds J. M. Bernardo, J. Berger, A. P. Dawid, and A. F. M. Smith), pp. 147– 167. Oxford: Oxford University Press. Gelfand, A. E. and Smith, A. F. M. (1990) Sampling-based approaches to calculating marginal densities. J. Am. Statist. Ass., 85, 398– 409. Gelfand, A. E. and Smith, A. F. M. (1991) Gibbs sampling for marginal posterior expectations. Communs Statist. Theory Meth., 20, 1747– 1766. Gelman, A. and Rubin, D. B. (1991) Honest inferences from iterative simulation. Technical Report 307. Department of Statistics, Harvard University, Cambridge. Gelman, A. and Rubin, D. B. (1992) Inference from iterative simulation using multiple sequences. Statist. Sci., to be published. Geman, S. and Geman, D. (1984) Stochastic relaxation, Gibbs distributions and the Bayesian restoration of images. IEEE Trans. Pattn Anal. Mach. Intell., 6, 721– 741. Geweke, J. (1988) Antithetic acceleration of Monte Carlo integration in Bayesian inference. J. Econometr., 38, 73– 90. Geweke, J. (1989) Inference and forecasting for deterministic nonlinear time series observed with measurement error. Technical Report. Duke University, Durham. Geweke, J. (1992) Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments. In Bayesian Statistics 4 (eds J. M. Bernardo, J. Berger, A. P. Dawid, and A. F. M. Smith), pp. 169– 194. Oxford: Oxford University Press. Geyer, C. J. (1991a) Markov chain Monte Carlo maximum likelihood. In Computer Science and Statistics: Proc. 23rd Symp. Interface (ed. E. M. Keramidas), pp. 156– 163. Fairfax Station: Interface Foundation. Geyer, C. J. (1991b) Reweighting Monte Carlo mixtures. Technical Report 568. School of Statistics, University of Minnesota, Minneapolis. Geyer, C. J. (1993) Practical Markov chain Monte Carlo. Statist. Sci., to be published. Geyer, C. J. and Thompson, E. A. (1992) Constrained Monte Carlo maximum likelihood for dependent data (with discussion). J. R. Statist. Soc. B, 54, 657– 699. Gigli, A. (1993) Contributions to importance sampling and resampling. PhD Thesis. Imperial College of Science, Technology and Medicine, London. Gilks, W. R., Best, N. G. and Tan, K. K. C. (1992a) Adaptive rejection Metropolis sampling. to be published. Gilks, W. R., Roberts, G. O. and George, E. (1992b) Adaptive direction sampling. to be published. Gilks, W. R. and Wild, R. (1992) Adaptive rejection sampling for Gibbs sampling. Appl. Statist., 41, 337– 348. Goodall, C. R. and Jona-Lasinio, G. D. (1992) Bayesian estimation for graphical Gaussian models by projection and data augmentation. to be published. Goodman, J. and Sokal, A. D. (1989) Multigrid Monte Carlo method: conceptual foundations. Phys. Rev. D, 40, 2035– 2071. Gray, A. J. (1992) Simulating posterior Gibbs distributions: A comparison of the Swendsen-Wang and Gibbs sampler methods. to be published. Green, P. J. and Han, X.-L. (1992) Metropolis methods, gaussian proposals, and antithetic variables. Lect. Notes Statist., 74, 142– 164. Greig, D. M., Porteous, B. T. and Seheult, A. H. (1989) Exact maximum a posteriori estimation for binary images. J. R. Statist. Soc. B, 51, 271– 279. Hammersley, J. M. and Handscomb, D. C. (1967) Monte Carlo Methods, ch. 11, p. 134. Norwich: Fletcher. Harvey, A. C. (1989) Forecasting, Structural Time Series Models and the Kalman Filter, pp. 162– 165. Cambridge: Cambridge University Press. Heitjan, D. F. and Rubin, D. B. (1991) Ignorability and coarse data. Ann. Statist., 19, 2244– 2253. Hills, S. E. and Smith, A. F. M. (1992) Parameterization issues in Bayesian inference. In Bayesian Statistics 4 (eds J. M. Bernardo, J. Berger, A. P. Dawid, and A. F. M. Smith), pp. 227– 246. Oxford: Oxford University Press. Hopfield, J. J. (1982) Neural networks and physical systems with emergent collective computational abilities. Proc. Natn. Acad. Sci. USA, 79, 2554– 2558. Hopfield, J. J. and Tank, D. W. (1985) “Neural” computation of decisions in optimization problems. Biol. Cybernet., 52, 141– 152. Hout, M., Duncan, O. D. and Sobel, M. E. (1987) Association and heterogeneity: structural models of similarities and differences. Sociol. Meth., 17, 145– 184. Isham, V. (1993) Some statistical aspects of chaos: A review. In Chaos and Networks: Statistical and Probabilistic Aspects (eds O. E. Barndorff-Nielsen, D. R. Cox, J. L. Jensen and W. S. Kendall). London: Chapman and Hall. to be published. Jerrum, M. and Sinclair, A. (1989) Approximating the permanent. SIAM J. Comput., 1, 1149– 1178. Jerrum, M. and Sinclair, A. (1990) Polynomial-time approximation algorithm for the Ising Model. Internal Report. Department of Computer Science, University of Edinburgh, Edinburgh. Jones, M. C. (1987) Randomly choosing parameters from the stationarity and invertibility region of autoregressive-moving average models. Appl. Statist., 36, 134– 138. Kalbfleisch, J. D. (1978) Non-parametric Bayesian analysis of survival time data. J. R. Statist. Soc. B, 40, 214– 221. Kelton, W. D. and Law, A. M. (1984) The analytical evaluation of alternative strategies in steady-state simulation. J Ops Res., 32, 169– 184. Kipnis, C. and Varadhan, S. R. S. (1986) Central limit theorem for additive functionals of reversible Markov processes and applications to simple exclusions. Communs Math. Phys., 104, 1– 19. Kolassa, J. E. and Tanner, M. A. (1992) Approximate frequentist inference via the Gibbs sampler. Technical Report. Department of Biostatistics, University of Rochester, Rochester. Kong, A., Liu, J. and Wong, W. H. (1991) Sequential imputations and Bayesian missing data problems. Technical Report 321. Department of Statistics, University of Chicago, Chicago. Künsch, H. R. (1987) Intrinsic auto regressions and related models on the two-dimensional lattice. Biometrika, 74, 517– 524. Lange, K. and Matthysse, S. (1989) Simulation of pedigree genotypes by random walks. Am. J. Hum. Genet., 45, 959– 970. Lauritzen, S. L. (1990) Propagation of probabilities, means and variances in mixed graphical association models. Technical Report R90-18. Department of Mathematics and Computer Science, University of Aalborg, Aalborg. Lauritzen, S. L., Dawid, A. P., Larsen, B. N. and Leimer, H.-G. (1990) Independence properties of directed Markov fields. Networks, 20, 491– 505. Lawler, G. F. and Sokal, A. D. (1988) Bounds on the L2 spectrum for Markov chains and Markov processes: A generalization of Cheeger's inequality. Trans. Am. Math. Soc., 309, 557– 580. Lawson, A. B. (1992) Gibbs sampling a spatial Cox process. Submitted to J. R. Statist. Soc. B. Li, X.-J. and Sokal, A. D. (1989) Rigorous lower bound on the dynamic critical exponents of the Swendsen-Wang algorithm. Phys. Rev. Lett., 63, 827– 830. Li, X.-J. and Sokal, A. D. (1991) Rigorous lower bound on the dynamic critical exponent of some multilevel Swendsen-Wang algorithms. Phys. Rev. Lett., 67, 1482– 1485. Liu, J. (1992) The collapsed Gibbs sampler and other issues: with applications to a protein binding problem. Technical Report. Department of Statistics, Harvard University, Cambridge. Liu, J., Wong, W. and Kong, A. (1991a) Correlation structure and convergence rate of the Gibbs sampler with various scans. Technical Report. Department of Statistics, Harvard University, Cambridge. Liu, J., Wong, W. and Kong, A. (1991b) Correlation structure and convergence rate of the Gibbs sampler. Technical Reports 299 and 304. Department of Statistics. University of Chicago, Chicago. Lovász, L. and Simonovits, M. (1990) The mixing rate of Markov chains, an isoperimetric inequality, and computing the volume. In Proc. 31st IEEE Symp. Foundations of Computer Science, pp. 346– 355. Madigan, D. and Kong, A. (1992) A note on Bayesian accounting for model uncertainty with missing data. to be published. Mardia, K. V., Hainsworth, T. J. and Haddon, J. (1992) Deformable templates in image sequences. In Proc. 11th IAPR Conf., The Hague. Los Alamitos: IEEE Computer Society Press. Mardia, K. V., Kent, J. T. and Walder, A. W. (1991) Statistical shape models in image analysis. In Computer Science and Statistics: Proc. 23rd Symp. Interface (ed. E. M. Keramidas), pp. 550– 557. Fairfax Station: Interface Foundation. de la Mare, W. K. (1989) The model used in the Hitter and Fitter program. Rep. Int. Whaling Commissn, 39, 150– 151. Marinari, E. and Parisi, G. (1992) Simulated tempering: A new Monte Carlo scheme. Submitted to Europhys. Lett. Marriott, J. M., Ravishanker, N., Gelfand, A. E. and Pai, J. (1992) Bayesian analysis of ARMA processes: complete sampling based inference under full likelihoods. Research Report. Department of Statistics, University of Connecticut, Storrs. Matthews, P. (1991) A slowly mixing Markov chain with implications for Gibbs sampling. Technical Report. Department of Mathematics and Statistics, University of Maryland, Baltimore. Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N., Teller, A. H. and Teller, E. (1953) Equations of state calculations by fast computing machines. J. Chem. Phys., 21, 1087– 1092. Møller, J. (1992) Extensions of the Swendsen-Wang algorithm for simulating spatial point processes. to be published. Muller, P. (1991) A generic approach to posterior integration and Gibbs sampling. Preprint. Department of Statistics, Duke University, Durham. Newton, M. A. and Raftery, A. E. (1991) Approximate Bayesian inference by the weighted likelihood bootstrap. Submitted to J. R. Statist. Soc. B. Niedermayer, F. (1988) General cluster updating method for Monte Carlo simulations. Phys. Rev. Lett., 61, 2026– 2029. Patefield, W. M. (1981) Algorithm AS 159: An efficient method of generating r × c tables with given row and column totals. Appl. Statist., 30, 91– 97. Phillips, D. and Smith, A. F. M. (1992a) Orthogonal random-direction sampling in Markov chain Monte Carlo. Technical Report. Department of Mathematics, Imperial College of Science, Technology and Medicine, London. Phillips, D. and Smith, A. F. M. (1992b) Bayesian faces. Technical Report. Department of Mathematics, Imperial College of Science, Technology and Medicine, London. Piekaar, H. W. and Clarenburg, L. A. (1967) Aerosol filters—pore size distribution in fibrous filters. Chem. Engng Sci., 22, 1399– 1408. Qian, W. and Titterington, D. M. (1991) Estimation of parameters in hidden Markov models. Phil. Trans. R. Soc. Lond. A, 337, 407– 428. Racine, A., Grieve, A. P., Flühler, H. and Smith, A. F. M. (1986) Bayesian methods in practice: experiences in the pharmaceutical industry (with discussion). Appl. Statist., 35, 93– 150. Raftery, A. and Lewis, S. (1992) How many iterations in the Gibbs sampler? In Bayesian Statistics 4 (eds J. M. Bernardo, J. Berger, A. P. Dawid, and A. F. M. Smith), pp. 765– 776. Oxford: Oxford University Press. Robert, C. P. (1992) Discussion on Recent extensions to the EM algorithm (by X.-L. Meng and D. B. Rubin). In Bayesian Statistics 4 (eds J. M. Bernardo, J. Berger, A. P. Dawid, and A. F. M. Smith), pp. 315– 318. Oxford: Oxford University Press. Robert, C. P., Celeux, G. and Diebolt, J. (1992) Hidden Markov chains: A stochastic implementation. Technical Report LSTA 161. Université de Paris 6, Paris. Roberts, G. O. (1992) Convergence diagnostics of the Gibbs sampler. In Bayesian Statistics 4 (eds J. M. Bernardo, J. Berger, A. P. Dawid, and A. F. M. Smith), pp. 777– 784. Oxford: Oxford University Press. Roberts, G. O. and Gilks, W. R. (1992) Convergence of adaptive direction sampling. to be published. Roberts, G. O. and Hills, S. E. (1992) Assessing distributional convergence of the Gibbs sampler. Submitted to J. Am. Statist. Ass. Rosenthal, J. S. (1991a) Rates of convergence for data augmentation on finite sample spaces. Technical Report. Department of Mathematics, Harvard University, Cambridge. Rosenthal, J. S. (1991b) Rates of convergence for Gibbs sampling for variance components models. Technical Report. Department of Mathematics, Harvard University, Cambridge. Rubin, D. B. (1987) The SIR algorithm—a discussion of Tanner and Wong's: The calculation of posterior distributions by data augmentation. J. Am. Statist. Ass., 82, 543– 546. Rubin, D. B. (1988) Using the SIR algorithm to simulate posterior distributions. In Bayesian Statistics 3 (eds J. M. Bernardo, M. H. DeGroot, D. V. Lindley, and A. F. M. Smith), pp. 395– 402. Oxford: Oxford University Press. Ruelle, D. (1989) Chaotic Evolution and Strange Attractors, pp. 58– 60. Cambridge: Cambridge University Press. Sadowsky, J. S. and Bucklew, J. A. (1990) On large deviation theory and asymptotically efficient Monte Carlo estimation. IEEE Trans. Inform. Theory, 36. Schmeiser, B. and Chen, M.-H. (1992) On random-direction Monte Carlo sampling for evaluating multidimensional integrals. Technical Report. Purdue University, West Lafayette. Sheehan, N. and Thomas, A. W. (1992) On the irreducibility of a Markov chain defined on a space of genotype configurations by a sampling scheme. Biometrics, to be published. Shumway, R. H. and Stoffer, D. S. (1982) An approach to time series smoothing and forecasting using the EM algorithm. J. Time Ser. Anal., 3, 253– 264. Silverman, B. W. (1986) Density Estimation for Statistics and Data Analysis. London: Chapman and Hall. Sinclair, A. and Jerrum, M. (1989) Approximate counting, uniform generation and rapidly mixing Markov chains. Inform. Comput., 82, 93– 133. Sinha, D. (1993a) Semiparametric Bayesian analysis of multiple event time data. J. Am. Statist. Ass., 88, in the press. Sinha, D. (1993b) Nonparametric Bayesian analysis of interval-censored data. to be published. Skovgaard, I. M. (1987) Saddlepoint expansions for conditional distributions. J. Appl. Probab., 24, 875– 887. Smith, A. F. M. and Gelfand, A. E. (1992) Bayesian Statistics without tears: A sampling-resampling perspective. Am. Statistn., 46, 84– 88. Smith, A. F. M., Skene, A. M., Shaw, J. E. H. and Naylor, J. C. (1987) Progress with numerical and graphical methods for practical Bayesian statistics. Statistician, 36, 75– 82. Smolensky, P. (1986) Information processing in dynamical systems: foundations of Harmony Theory. In Parallel Distributed Processing (eds D. E. Rumelhart et al.), vol. I, pp. 194– 281. Cambridge: Massachusetts Institute of Technology Press. Sokal, A. D. (1989) Monte Carlo methods in statistical mechanics: foundations and new algorithms. Cours de Troisième Cycle de la Physique en Suisse Romande. Lausanne. Sokal, A. D. (1991) How to beat critical slowing-down: 1990 update. Nucl. Phys. B, 20, suppl., 55– 67. Sokal, A. D. and Thomas, L. E. (1989) Exponential convergence to equilibrium for a class of random-walk models. J. Statist. Phys., 54, 797– 828. Stiratelli, R., Laird, N. and Ware, J. H. (1984) Random-effects models for serial observations with binary response. Biometrics, 40, 961– 971. Strauss, D. (1975) A model for clustering. Biometrika, 62, 467– 475. Tanner, M. A. (1991) Tools for statistical inference, observed data and data augmentation methods. Lect. Notes Statist., 67. Tanner, M. and Wong, W. (1987) The calculation of posterior distributions by data augmentation (with discussion). J. Am. Statist. Ass., 82, 528– 550. Thompson, E. A. and Wijsman, E. M. (1990) The Gibbs sampler on extended pedigrees: Monte Carlo methods for the genetic analysis of complex traits. Technical Report 193. Department of Statistics, University of Washington, Seattle. Tierney, L. (1991) Exploring posterior distributions using Markov chains. In Computer Science and Statistics: Proc. 23rd Symp. Interface (ed. E. M. Keramidas), pp. 563– 570. Fairfax Station: Interface Foundation. H. Tong and R. L. Smith (eds) (1992) Royal Statistical Society meeting on chaos. J. R. Statist. Soc. B, 54, 301– 474. Tóth, B. (1986) Persistent random walks in random environment. Probab. Theory Reltd Fields, 71, 615– 625. Wakefield, J. C. (1992) Discussion on Parameterization issues in Bayesian inference (by S. E. Hills and A. F. M. Smith). In Bayesian Statistics 4 (eds J. M. Bernardo, J. Berger, A. P. Dawid, and A. F. M. Smith), pp. 243– 244. Oxford: Oxford University Press. Wakefield, J. C., Gelfand, A. E. and Smith, A. F. M. (1991) Efficient generation of random variates via the ratio-of-uniforms technique. Statist. Comput., 1, 129– 133. Wei, G. C. G. and Tanner, M. A. (1990) A Monte-Carlo implementation of the EM algorithm and the poor man's data augmentation algorithms. J. Am. Statist. Ass., 85, 699– 704. West, M. (1992a) Bayesian computations: Monte Carlo density estimation. Submitted to J. R. Statist. Soc. B. West, M. (1992b) Modelling with mixtures. In Bayesian Statistics 4 (eds J. M. Bernardo, J. Berger, A. P. Dawid, and A. F. M. Smith), pp. 503– 524. Oxford: Oxford University Press. Whitt, W. (1991) The efficiency of one long run versus independent replications in steady-state simulation. Mangmt Sci., 37, 645– 666. Wolff, U. (1989) Collective Monte Carlo updating for spin systems. Phys. Rev. Lett., 62, 361– 364. Citing Literature Volume55, Issue1September 1993Pages 53-102 This article also appears in:Discussion Papers ReferencesRelatedInformation