Abstract
To simulate a multivariate density with multi-hump, Markov chain Monte Carlo method encounters the obstacle of escaping from one hump to another, since it usually takes extraordinately long time and then becomes practically impossible to perform. To overcome these difficulties, a reversible scheme to generate a Markov chain, in terms of which the simulated density may be successful in rather general cases of practically avoiding being trapped in local humps, was suggested.
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Besag, J., Green, P. J., Spatial statistics and Bayesian computation, J. R. Statist. Soc. B, 1993, 55(1): 25.
Chen, D., Qian, M. P., Metastability of exponentially perturbed Markov chains, Science in China, Series A, 1996, 39(1):7.
Gelman, A., Rubin, D. B., Inference from iterative simulation using multiple sequences, Statist. Soc., 1992, 7(4): 457.
Gelman, A., Rubin, D. B., A single series from the Gibbs sampler provides a false sense of security, in Bayesian Statistics 4 (eds. Bernardo, J. M., Berger, J., Dawid, A. P. et al.), Oxford; Oxford University Press, 1992, 627–633.
Geweke, J., Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments, in Bayesian Statistics 4 (eds. Bernardo, J. M., Berger, J. O., Dawid, A. P. et al.), Oxford: Oxford University Press, 1992, 169–193.
Schervish, M. J., Carlin, B. P., On the convergence of successive substitution sampling, J. Comp. Graph. Statist., 1992, 1(2): 111.
Roberts, G. O., Poison, N. G., On the geometric convergence of the Gibbs sampler, J. R. Statist. Soc. B, 1994, 56(2): 377.
Tierney, L., Markov chains for exploring posterior distributions, Ann. Stat., 1994, 24(4): 1701.
Diaconis, P., Stroock, D., Geometric bounds for eigenvalues of Markov chains, Ann. Appl. Prob., 1991, 1(1): 36.
Liu, J., Wong, W. H., Kong, A., Covariance structure and convergence rate of the Gibbs sampler with various scan, J. R. Statist. Soc. B, 1995, 57(1): 104.
Rosenthal, J. S., Rates of convergence for Gibbs sampling for variance component models, Ann. of Statist., 1995, 23(3): 740.
Baldi, P., Frigessi, A., Piccioni, M., Importance sampling for Gibbs random fields, Ann. Appl. Prob., 1993, 3(2): 914.
Carlin, B. P., Gelfand, A. E., Smith, A. F. M., Hierarchical Bayesian analysis of change point problems, Appl. Statist., 1993, 41(1): 389.
Carlin, B. P., Chib, S., Bayesian model choice via Markov chain Monte Carlo methods, J. R. Statist. Soc. B, 1995, 57(3): 473.
Ferrari, P. A., Frigessi, A., Schonmann, R, H., Convergence of some partially parallel Gibbs samplers with annealing, Ann. Appl. Prob., 1993, 3(l): 137.
Gilks, W. R., Clayto, D. G., Spiegelhalter, D. J. et al., Modelling complexity: Applications of Gibbs sampling in medicine, J. R. Statist. Soc. B, 1993, 55(1): 39.
Ingrassia, S., On the rate of convergence of the Metropolis algorithm and Gibbs sampler by geometric bounds, Ann. Appl. Prob., 1994, 4(1): 347.
Roberts, G. O., Smith, A, F. M., Simple conditions for the convergence of the Gibbs sampler and Metropolis- Hastings algorithms, Stoch. Processes Appl., 1994, 49(1): 207.
Smith, A. F. M., Roberts, G, O., Bayesian computation via the Gibbs sampler and related Markov chain Monte Carlo methods, J. R. Statist. Soc. B, 1993, 55(1): 3.
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Gong, G., Qian, M. & Xie, J. Reversible algorithm of simulating multivariate densities with multi-hump. Sci. China Ser. A-Math. 44, 357–364 (2001). https://doi.org/10.1007/BF02878717
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DOI: https://doi.org/10.1007/BF02878717