Reversible algorithm of simulating multivariate densities with multi-hump. (English) Zbl 0997.60076
Summary: 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, is suggested.
MSC:
| 60J22 | Computational methods in Markov chains |
| 60J10 | Markov chains (discrete-time Markov processes on discrete state spaces) |
| 65C05 | Monte Carlo methods |
References:
| [1] | Besag, J.; Green, P. J., Spatial statistics and Bayesian computation, J. R. Statist. Soc. B, 55, 1, 25-25 (1993) · Zbl 0800.62572 |
| [2] | Chen, D.; Qian, M. P., Metastability of exponentially perturbed Markov chains, Science in China, Series A, 39, 1, 7-7 (1996) · Zbl 0863.60065 |
| [3] | Gelman, A.; Rubin, D. B., Inference from iterative simulation using multiple sequences, Statist. Soc., 7, 4, 457-457 (1992) · Zbl 1386.65060 · doi:10.1214/ss/1177011136 |
| [4] | Gelman, A.; Rubin, D. B.; Bernardo, J. M.; Berger, J.; Dawid, A. P., A single series from the Gibbs sampler provides a false sense of security, Bayesian Statistics 4, 627-633 (1992), Oxford: Oxford University Press, Oxford |
| [5] | Geweke, J.; Bernardo, J. M.; Berger, J. O.; Dawid, A. P., Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments, Bayesian Statistics 4, 169-193 (1992), Oxford: Oxford University Press, Oxford |
| [6] | Schervish, M. J.; Carlin, B. P., On the convergence of successive substitution sampling, J. Comp. Graph. Statist., 1, 2, 111-111 (1992) · doi:10.2307/1390836 |
| [7] | Roberts, G. O.; Poison, N. G., On the geometric convergence of the Gibbs sampler, J. R. Statist. Soc. B, 56, 2, 377-377 (1994) · Zbl 0796.62029 |
| [8] | Tierney, L., Markov chains for exploring posterior distributions, Ann. Stat., 24, 4, 1701-1701 (1994) · Zbl 0829.62080 · doi:10.1214/aos/1176325750 |
| [9] | Diaconis, P.; Stroock, D., Geometric bounds for eigenvalues of Markov chains, Ann. Appl. Prob., 1, 1, 36-36 (1991) · Zbl 0731.60061 · doi:10.1214/aoap/1177005980 |
| [10] | Liu, J.; Wong, W. H.; Kong, A., Covariance structure and convergence rate of the Gibbs sampler with various scan, J. R. Statist. Soc. B, 57, 1, 104-104 (1995) |
| [11] | Rosenthal, J. S., Rates of convergence for Gibbs sampling for variance component models, Ann. of Statist., 23, 3, 740-740 (1995) · Zbl 0841.62074 · doi:10.1214/aos/1176324619 |
| [12] | Baldi, P.; Frigessi, A.; Piccioni, M., Importance sampling for Gibbs random fields, Ann. Appl. Prob., 3, 2, 914-914 (1993) · Zbl 0780.60047 · doi:10.1214/aoap/1177005372 |
| [13] | Carlin, B. P.; Gelfand, A. E.; Smith, A. F. M., Hierarchical Bayesian analysis of change point problems, Appl. Statist., 41, 1, 389-389 (1993) · Zbl 0825.62408 |
| [14] | Carlin, B. P.; Chib, S., Bayesian model choice via Markov chain Monte Carlo methods, J. R. Statist. Soc. B, 57, 3, 473-473 (1995) · Zbl 0827.62027 |
| [15] | Ferrari, P. A.; Frigessi, A.; Schonmann, R, H., Convergence of some partially parallel Gibbs samplers with annealing, Ann. Appl. Prob., 3, l, 137-137 (1993) · Zbl 0771.60050 · doi:10.1214/aoap/1177005511 |
| [16] | Gilks, W. R.; Clayto, D. G.; Spiegelhalter, D. J., Modelling complexity: Applications of Gibbs sampling in medicine, J. R. Statist. Soc. B, 55, 1, 39-39 (1993) · Zbl 0779.62100 |
| [17] | Ingrassia, S., On the rate of convergence of the Metropolis algorithm and Gibbs sampler by geometric bounds, Ann. Appl. Prob., 4, 1, 347-347 (1994) · Zbl 0802.60061 · doi:10.1214/aoap/1177005064 |
| [18] | Roberts, G. O.; Smith, A, F. M., Simple conditions for the convergence of the Gibbs sampler and Metropolis- Hastings algorithms, Stoch. Processes Appl., 49, 1, 207-207 (1994) · Zbl 0803.60067 · doi:10.1016/0304-4149(94)90134-1 |
| [19] | 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, 55, 1, 3-3 (1993) · Zbl 0779.62030 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
