메뉴 건너뛰기




Volumn 16, Issue 4, 2001, Pages 340-350

Ordering and Improving the Performance of Monte Carlo Markov Chains

Author keywords

Asymptotic variance; Convergence ordering; Covariance ordering; Efficiency ordering; Metropolis Hastings algorithm; Peskun ordering; Reversible jumps

Indexed keywords


EID: 0042193001     PISSN: 08834237     EISSN: None     Source Type: Journal    
DOI: 10.1214/ss/1015346319     Document Type: Article
Times cited : (93)

References (41)
  • 2
    • 84864739618 scopus 로고
    • Monotone and convex operator functions
    • BENDAT, J. and SHERMAN, S. (1955). Monotone and convex operator functions. Trans. Amer. Math. Soc. 79 58-71.
    • (1955) Trans. Amer. Math. Soc. , vol.79 , pp. 58-71
    • Bendat, J.1    Sherman, S.2
  • 3
    • 0004020370 scopus 로고    scopus 로고
    • Technical Report 9, Center for Statistics and the Social Sciences. Available at www.csss.washington.edu/ papers/wp9.ps.
    • BESAG, J. (2000). Markov chain Monte Carlo for statistical inference. Technical Report 9, Center for Statistics and the Social Sciences. Available at www.csss.washington.edu/ papers/wp9.ps.
    • (2000) Markov Chain Monte Carlo for Statistical Inference
    • Besag, J.1
  • 4
    • 0000103562 scopus 로고
    • Spatial statistics and Bayesian computation
    • BESAG, J. and GREEN, P. J. (1993). Spatial statistics and Bayesian computation. J. Roy. Statist. Soc. Ser. B 55 25-37.
    • (1993) J. Roy. Statist. Soc. Ser. B , vol.55 , pp. 25-37
    • Besag, J.1    Green, P.J.2
  • 5
    • 0041386088 scopus 로고    scopus 로고
    • A geometric interpretation of the Metropolis algorithm
    • BILLERA, L. J. and DIACONIS, P. (2001). A geometric interpretation of the Metropolis algorithm. Statist. Sci. 16 335-339.
    • (2001) Statist. Sci. , vol.16 , pp. 335-339
    • Billera, L.J.1    Diaconis, P.2
  • 7
    • 0002205556 scopus 로고    scopus 로고
    • Rao-Blackwellization of sampling schemes
    • CASELLA, G. and ROBERT, C. P. (1996). Rao-Blackwellization of sampling schemes. Biometrika 83 81-94.
    • (1996) Biometrika , vol.83 , pp. 81-94
    • Casella, G.1    Robert, C.P.2
  • 8
    • 0036522630 scopus 로고    scopus 로고
    • Improving convergence of the Hastings-Metropolis algorithm with a learning proposal
    • To appear
    • CHAUVEAU, D. and VANDEKERKHOVE, P. (2001). Improving convergence of the Hastings-Metropolis algorithm with a learning proposal. Scand. J. Statist. To appear.
    • (2001) Scand. J. Statist.
    • Chauveau, D.1    Vandekerkhove, P.2
  • 9
    • 0034346693 scopus 로고    scopus 로고
    • Analysis of a nonreversible Markov chain sampler
    • DIACONIS, P., HOLMES, S. and NEAL, R. M. (2000). Analysis of a nonreversible Markov chain sampler. Ann. Appl. Probab. 10 726-752.
    • (2000) Ann. Appl. Probab. , vol.10 , pp. 726-752
    • Diaconis, P.1    Holmes, S.2    Neal, R.M.3
  • 10
    • 0000207240 scopus 로고
    • Convergence rates of the Gibbs sampler, the Metropolis algorithm and other single-site updating dynamics
    • FRIGESSI, A., DI STEFANO, P., HWANG, A. and SHEU, A. (1993). Convergence rates of the Gibbs sampler, the Metropolis algorithm and other single-site updating dynamics. J. Roy. Statist. Soc. Ser. B 55 205-219.
    • (1993) J. Roy. Statist. Soc. Ser. B , vol.55 , pp. 205-219
    • Frigessi, A.1    Di Stefano, P.2    Hwang, A.3    Sheu, A.4
  • 11
    • 0039092032 scopus 로고
    • Optimal spectral structure of reversible stochastic matrices, Monte Carlo methods and the simulation of Markov random fields
    • FRIGESSI, A., HWANG, C. 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.
    • (1992) Ann. Appl. Probab. , vol.2 , pp. 610-628
    • Frigessi, A.1    Hwang, C.2    Younes, L.3
  • 12
    • 84950453304 scopus 로고
    • Sampling based approaches to calculating marginal densities
    • GELFAND, A. E. and SMITH, A. F. M. (1990). Sampling based approaches to calculating marginal densities. J. Amer. Statist. Assoc. 85 398-409.
    • (1990) J. Amer. Statist. Assoc. , vol.85 , pp. 398-409
    • Gelfand, A.E.1    Smith, A.F.M.2
  • 13
    • 0032333313 scopus 로고    scopus 로고
    • Adaptive Markov chain Monte Carlo through regeneration
    • GILKS, W. R., ROBERTS, G. O. and SAHU, S. K. (1998). Adaptive Markov chain Monte Carlo through regeneration. J. Amer. Statist. Assoc. 93 1045-1054.
    • (1998) J. Amer. Statist. Assoc. , vol.93 , pp. 1045-1054
    • Gilks, W.R.1    Roberts, G.O.2    Sahu, S.K.3
  • 14
    • 77956889087 scopus 로고
    • Reversible jump Markov chain Monte Carlo computation and Bayesian model determination
    • GREEN, P. J. (1995). Reversible jump Markov chain Monte Carlo computation and Bayesian model determination. Biometrika 82 711-732.
    • (1995) Biometrika , vol.82 , pp. 711-732
    • Green, P.J.1
  • 15
    • 0042908796 scopus 로고    scopus 로고
    • Delayed rejection in reversible jump Metropolis-Hastings
    • GREEN, P. J. and MIRA, A. (2001). Delayed rejection in reversible jump Metropolis-Hastings. Biometrika 88 1035-1053.
    • (2001) Biometrika , vol.88 , pp. 1035-1053
    • Green, P.J.1    Mira, A.2
  • 16
    • 0030363220 scopus 로고    scopus 로고
    • Outperforming the Gibbs sampler empirical estimator for nearest-neighbor random fields
    • GREENWOOD, P. E., MCKEAGUE, I. W. and WEFELMEYER, W. (1996). Outperforming the Gibbs sampler empirical estimator for nearest-neighbor random fields. Ann. Statist. 24 1433-1456.
    • (1996) Ann. Statist. , vol.24 , pp. 1433-1456
    • Greenwood, P.E.1    McKeague, I.W.2    Wefelmeyer, W.3
  • 17
    • 21844523282 scopus 로고
    • Efficiency of empirical estimators for Markov chains
    • GREENWOOD, P. E. and WEFELMEYER, W. (1995). Efficiency of empirical estimators for Markov chains. Ann. Statist. 23 132-143.
    • (1995) Ann. Statist. , vol.23 , pp. 132-143
    • Greenwood, P.E.1    Wefelmeyer, W.2
  • 18
    • 0007291856 scopus 로고    scopus 로고
    • Reversible Markov chains and optimality of symmetrized empirical estimators
    • GREENWOOD, P. E. and WEFELMEYER, W. (1999). Reversible Markov chains and optimality of symmetrized empirical estimators. Bernoulli 5 109-123.
    • (1999) Bernoulli , vol.5 , pp. 109-123
    • Greenwood, P.E.1    Wefelmeyer, W.2
  • 19
    • 0033436531 scopus 로고    scopus 로고
    • Adaptive proposal distribution for random walk Metropolis algorithm
    • HAARIO, H., SAKSMAN, E. and TAMMINEN, J. (1999). Adaptive proposal distribution for random walk Metropolis algorithm. Comput. Statist. 14 375-395.
    • (1999) Comput. Statist. , vol.14 , pp. 375-395
    • Haario, H.1    Saksman, E.2    Tamminen, J.3
  • 20
    • 0038563932 scopus 로고    scopus 로고
    • An adaptive Metropolis algorithm
    • HAARIO, H., SAKSMAN, E. and TAMMINEN, J. (2001). An adaptive Metropolis algorithm. Bernoulli 7 223-242.
    • (2001) Bernoulli , vol.7 , pp. 223-242
    • Haario, H.1    Saksman, E.2    Tamminen, J.3
  • 21
    • 0003573107 scopus 로고    scopus 로고
    • Technical Report SAND/ 11/98, Norwegian Computing Center. Available at www.maths.surrey.ac.uk/personal/st/S.Brooks/MCMC
    • HOLDEN, L. (1998). Adaptive chains. Technical Report SAND/ 11/98, Norwegian Computing Center. Available at www.maths.surrey.ac.uk/personal/st/S.Brooks/MCMC/.
    • (1998) Adaptive Chains
    • Holden, L.1
  • 22
    • 21344458535 scopus 로고    scopus 로고
    • Metropolized independent sampling
    • LIU, J. S. (1996a). Metropolized independent sampling. Statist. Comput. 6 113-119.
    • (1996) Statist. Comput. , vol.6 , pp. 113-119
    • Liu, J.S.1
  • 23
    • 0008766414 scopus 로고    scopus 로고
    • Peskun theorem and a modified discrete-state Gibbs sampler
    • LIU, J. S. (1996b). Peskun theorem and a modified discrete-state Gibbs sampler. Biometrika 83 681-682.
    • (1996) Biometrika , vol.83 , pp. 681-682
    • Liu, J.S.1
  • 24
    • 0000854270 scopus 로고
    • Correlation structure and convergence rate of the Gibbs sampler with various scans
    • LIU, J. S., WONG, W. H. and KONG, A. (1995). Correlation structure and convergence rate of the Gibbs sampler with various scans. J. Roy. Statist. Soc. Ser. B 57 157-169.
    • (1995) J. Roy. Statist. Soc. Ser. B , vol.57 , pp. 157-169
    • Liu, J.S.1    Wong, W.H.2    Kong, A.3
  • 25
    • 34250967722 scopus 로고
    • Über monotone Matrixfunktionen
    • LÖWNER, K. (1934). Über monotone Matrixfunktionen. Math. Z. 38 177-216.
    • (1934) Math. Z. , vol.38 , pp. 177-216
    • Löwner, K.1
  • 26
    • 0042916615 scopus 로고    scopus 로고
    • Markov chain Monte Carlo and Rao-Blackvvellization
    • MCKEAGUE and WEFELMEYER (2000). Markov chain Monte Carlo and Rao-Blackvvellization. J. Statist. Plann. Inf. 85 171-182.
    • (2000) J. Statist. Plann. Inf. , vol.85 , pp. 171-182
    • McKeague1    Wefelmeyer2
  • 27
    • 0042908795 scopus 로고    scopus 로고
    • Efficiency increasing and stationarity preserving probability mass transfers for MCMC
    • To appear
    • MIRA, A. (2001a). Efficiency increasing and stationarity preserving probability mass transfers for MCMC. Statist. Probab. Lett. To appear.
    • (2001) Statist. Probab. Lett.
    • Mira, A.1
  • 28
    • 84891435216 scopus 로고    scopus 로고
    • On Metropolis-Hastings algorithms with delayed rejection
    • To appear
    • MIRA, A. (2001b). On Metropolis-Hastings algorithms with delayed rejection. Metron. To appear.
    • (2001) Metron.
    • Mira, A.1
  • 29
    • 0004174671 scopus 로고    scopus 로고
    • Technical Report 632, School of Statistics, Univ. Minnesota. Available at aim.unipv.it/∼anto/order.ps.
    • MIRA, A. and GEYER, C. J. (1999). Ordering Monte Carlo Markov chains. Technical Report 632, School of Statistics, Univ. Minnesota. Available at aim.unipv.it/∼anto/order.ps.
    • (1999) Ordering Monte Carlo Markov Chains.
    • Mira, A.1    Geyer, C.J.2
  • 30
    • 0042508062 scopus 로고    scopus 로고
    • On non-reversible Markov chains
    • MIRA, A. and GEYER, C. J. (2000). On non-reversible Markov chains. Fields Inst. Comm. 26 93-108.
    • (2000) Fields Inst. Comm. , vol.26 , pp. 93-108
    • Mira, A.1    Geyer, C.J.2
  • 32
    • 0036005408 scopus 로고    scopus 로고
    • Efficiency and convergence properties of slice samplers
    • MIRA, A. and TIERNEY, L. (2001). Efficiency and convergence properties of slice samplers. Scand. J. Statist. 29 1035-1053.
    • (2001) Scand. J. Statist. , vol.29 , pp. 1035-1053
    • Mira, A.1    Tierney, L.2
  • 33
    • 0001692404 scopus 로고    scopus 로고
    • Suppressing random walks in Markov chain Monte Carlo using ordered overrelaxation
    • M. I. Jordan, ed. Kluwer Academic, Dordrecht
    • NEAL, R. M. (1998). Suppressing random walks in Markov chain Monte Carlo using ordered overrelaxation. In Learning in Graphical Models (M. I. Jordan, ed.) 205-225. Kluwer Academic, Dordrecht.
    • (1998) Learning in Graphical Models , pp. 205-225
    • Neal, R.M.1
  • 34
    • 0015730787 scopus 로고
    • Optimum Monte Carlo sampling using Markov chains
    • PESKUN, P. H. (1973). Optimum Monte Carlo sampling using Markov chains. Biometrika 60 607-612.
    • (1973) Biometrika , vol.60 , pp. 607-612
    • Peskun, P.H.1
  • 35
    • 0001974429 scopus 로고    scopus 로고
    • Markov chain concepts related to sampling algorithms
    • W. R. Gilks, S. Richardson and D. J. Spiegelhalter, eds.. Chapman and Hall, New York
    • ROBERTS, G. O. (1996). Markov chain concepts related to sampling algorithms. In Markov Chain Monte Carlo in Practice (W. R. Gilks, S. Richardson and D. J. Spiegelhalter, eds.). Chapman and Hall, New York.
    • (1996) Markov Chain Monte Carlo in Practice
    • Roberts, G.O.1
  • 36
    • 0000051645 scopus 로고    scopus 로고
    • Updating schemes, covariance structure, blocking and parametrisation for the Gibbs sampler
    • ROBERTS, G. O. and SAHU, S. K. (1997). Updating schemes, covariance structure, blocking and parametrisation for the Gibbs sampler. J. Roy. Statist. Soc. Ser. B 59 291-317.
    • (1997) J. Roy. Statist. Soc. Ser. B , vol.59 , pp. 291-317
    • Roberts, G.O.1    Sahu, S.K.2
  • 37
    • 0035609585 scopus 로고    scopus 로고
    • Approximate pre-determined convergence properties of the Gibbs sampler
    • ROBERTS, G. O. and SAHU, S. K. (2001). Approximate pre-determined convergence properties of the Gibbs sampler. J. Comput. Graph. Statist. 10 216-229.
    • (2001) J. Comput. Graph. Statist. , vol.10 , pp. 216-229
    • Roberts, G.O.1    Sahu, S.K.2
  • 38
    • 0041375875 scopus 로고    scopus 로고
    • On convergence of the EM algorithm and the Gibbs sampler
    • SAHU, S. K. and ROBERTS, G. O. (1999). On convergence of the EM algorithm and the Gibbs sampler. Statist. Comput. 9 55-64.
    • (1999) Statist. Comput. , vol.9 , pp. 55-64
    • Sahu, S.K.1    Roberts, G.O.2
  • 39
    • 0000576595 scopus 로고
    • Markov chains for exploring posterior distributions
    • TIERNEY, L. (1994). Markov chains for exploring posterior distributions. Ann. Statist. 22 1701-1762.
    • (1994) Ann. Statist. , vol.22 , pp. 1701-1762
    • Tierney, L.1
  • 40
    • 0032382065 scopus 로고    scopus 로고
    • A note on Metropolis-Hastings kernels for general state spaces
    • TIERNEY, L. (1998). A note on Metropolis-Hastings kernels for general state spaces. Ann. Appl. Probab. 8 1-9.
    • (1998) Ann. Appl. Probab. , vol.8 , pp. 1-9
    • Tierney, L.1
  • 41
    • 0033619197 scopus 로고    scopus 로고
    • Some adaptive Monte Carlo methods for Bayesian inference
    • TIERNEY, L. and MIRA, A. (1999). Some adaptive Monte Carlo methods for Bayesian inference. Statist. Med. 18 2507-2515.
    • (1999) Statist. Med. , vol.18 , pp. 2507-2515
    • Tierney, L.1    Mira, A.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.