메뉴 건너뛰기




Volumn 6, Issue 2, 2000, Pages 215-242

Estimating the second largest eigenvalue of a Markov transition matrix

Author keywords

Gibbs sampler; Hubert schmidt operator; Markov chain monte carlo; Metropolishastings algorithm

Indexed keywords


EID: 0007291056     PISSN: 13507265     EISSN: None     Source Type: Journal    
DOI: 10.2307/3318575     Document Type: Article
Times cited : (22)

References (28)
  • 1
    • 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
  • 3
    • 0002740591 scopus 로고
    • Geometric bounds for eigenvalues of Markov chains
    • Diaconis, P. and Stroock, D. (1991) Geometric bounds for eigenvalues of Markov chains. Ann. Appl. Probab., 1, 36-61.
    • (1991) Ann. Appl. Probab. , vol.1 , pp. 36-61
    • Diaconis, P.1    Stroock, D.2
  • 5
    • 0000207240 scopus 로고
    • Convergence rates of the Gibbs sampler, the Metropolis algorithm and other single-site updating dynamics
    • Frigessi, A., di Stefano, P., Hwang, C.-R. and Sheu, S.-J., (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, C.-R.3    Sheu, S.-J.4
  • 6
    • 0023287238 scopus 로고
    • Robust empirical Bayes analysis of event rates
    • Gaver, O.P. and O'Muircheartaigh, I.G. (1987) Robust empirical Bayes analysis of event rates. Technometrics, 29, 1-15.
    • (1987) Technometrics , vol.29 , pp. 1-15
    • Gaver, O.P.1    O'Muircheartaigh, I.G.2
  • 7
    • 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
  • 8
    • 84972492387 scopus 로고
    • Inference from iterative simulation using multiple sequences
    • Gelman, A. and Rubin, D.B. (1992) Inference from iterative simulation using multiple sequences. Statist. Sei., 7, 457-472.
    • (1992) Statist. Sei. , vol.7 , pp. 457-472
    • Gelman, A.1    Rubin, D.B.2
  • 9
    • 0021518209 scopus 로고
    • Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images
    • Geman, S. and Geman, D. (1984) Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images. IEEE Trans. Pattern Anal. Machine Intelligence, 6, 721-741.
    • (1984) IEEE Trans. Pattern Anal. Machine Intelligence , vol.6 , pp. 721-741
    • Geman, S.1    Geman, D.2
  • 10
    • 84972511893 scopus 로고
    • Practical Markov chain Monte Carlo
    • Geyer, C.J. (1992) Practical Markov chain Monte Carlo. Statist. Sei., 7, 473-483.
    • (1992) Statist. Sei. , vol.7 , pp. 473-483
    • Geyer, C.J.1
  • 11
    • 0000051109 scopus 로고
    • Constrained Monte Carlo maximum likelihood for dependent data (with discussion)
    • Geyer, C.J. and Thompson, E.A. (1992) Constrained Monte Carlo maximum likelihood for dependent data (with discussion). J. Roy. Statist. Soc. Ser. B. 54, 657-699.
    • (1992) J. Roy. Statist. Soc. Ser. B. , vol.54 , pp. 657-699
    • Geyer, C.J.1    Thompson, E.A.2
  • 12
    • 77956890234 scopus 로고
    • Monte Carlo sampling methods using Markov chains and their applications
    • Hastings, W.K. (1970) Monte Carlo sampling methods using Markov chains and their applications. Biometrika, 57, 97-109.
    • (1970) Biometrika , vol.57 , pp. 97-109
    • Hastings, W.K.1
  • 13
    • 34250130646 scopus 로고
    • Central limit theorem for additive functionals of reversible Markov processes and applications to simple exclusions
    • Kipnis, C. and Varadhan, S.R.S: (1986) Central limit theorem for additive functionals of reversible Markov processes and applications to simple exclusions. Com Math. Phys., 104, 1-19.
    • (1986) Com Math. Phys. , vol.104 , pp. 1-19
    • Kipnis, C.1    Varadhan, S.R.S.2
  • 14
    • 0000941412 scopus 로고
    • Bounds on the 2;2 spectrum for Markov chains and Markov processes: A generalization of Cheeger's inequality
    • Lawler, G.F. and Sokal, A.D. (1988) Bounds on the 2;2 spectrum for Markov chains and Markov processes: a generalization of Cheeger's inequality. Trans. Amer. Math. Soc., 309, 557-580.
    • (1988) Trans. Amer. Math. Soc. , vol.309 , pp. 557-580
    • Lawler, G.F.1    Sokal, A.D.2
  • 17
    • 0000759236 scopus 로고
    • How many iterations in the Gibbs sampler?
    • J.M. Bernardo, J.O. Berger, A.P. Dawid and A.F.M. Smith (eds), New York: Oxford University Press.
    • Raftery, A.E. and Lewis, S.M. (1992) How many iterations in the Gibbs sampler? In J.M. Bernardo, J.O. Berger, A.P. Dawid and A.F.M. Smith (eds), Bayesian Statistics 4, pp. 763-773. New York: Oxford University Press.
    • (1992) Bayesian Statistics , vol.4 , pp. 763-773
    • Raftery, A.E.1    Lewis, S.M.2
  • 18
    • 0000569335 scopus 로고
    • Convergence diagnostics of the Gibbs sampler
    • J.M. Bernardo, J.O. Berger, A.P. Dawid and A.F.M. Smith (eds), New York: Oxford University Press.
    • Roberts, G.O. (1992) Convergence diagnostics of the Gibbs sampler. In J.M. Bernardo, J.O. Berger, A.P. Dawid and A.F.M. Smith (eds), Bayesian Statistics 4, pp. 775-782. New York: Oxford University Press.
    • (1992) Bayesian Statistics , vol.4 , pp. 775-782
    • Roberts, G.O.1
  • 19
    • 0009000215 scopus 로고
    • Methods for estimating L2 convergence of Markov chain Monte Carlo
    • D. Berry, K. .Chaloner, and J. Geweke (eds), Amsterdam: North Holland.
    • Roberts, G.O. (1994) Methods for estimating L2 convergence of Markov chain Monte Carlo. In D. Berry, K. .Chaloner, and J. Geweke (eds), Bayesian Statistics and Econometrics: Essays in Honor of Arnold Zellner. Amsterdam: North Holland.
    • (1994) Bayesian Statistics and Econometrics: Essays in Honor of Arnold Zellner.
    • Roberts, G.O.1
  • 20
    • 0001764140 scopus 로고
    • Rates of convergence for data augmentation of finite sample spaces
    • Rosenthal, J.S. (1993) Rates of convergence for data augmentation of finite sample spaces. Ann. Appl. Probab., 3, 819-839.
    • (1993) Ann. Appl. Probab. , vol.3 , pp. 819-839
    • Rosenthal, J.S.1
  • 21
    • 84923618271 scopus 로고
    • Minorization conditions and convergence rates for Markov chain Monte Carlo
    • Rosenthal, J.S. (1995) Minorization conditions and convergence rates for Markov chain Monte Carlo. J. Amer. Statist. Assoc., 90, 558-566.
    • (1995) J. Amer. Statist. Assoc. , vol.90 , pp. 558-566
    • Rosenthal, J.S.1
  • 22
    • 0024699930 scopus 로고
    • Approximate counting, uniform generation and rapidly mixing Markov chains
    • Sinclair, A. and Jerrum, M. (1989) Approximate counting, uniform generation and rapidly mixing Markov chains. Inform, and Comput., 82, 93-133.
    • (1989) Inform, and Comput. , vol.82 , pp. 93-133
    • Sinclair, A.1    Jerrum, M.2
  • 23
    • 0003053548 scopus 로고
    • Bayesian computation via the Gibbs sampler and related Markov chain Monte Carlo methods
    • Smith, A.F.M. and Roberts, G.O. (1993) Bayesian computation via the Gibbs sampler and related Markov chain Monte Carlo methods. J. Roy. Statist. Soc. Ser. B., 55, 3-23.
    • (1993) J. Roy. Statist. Soc. Ser. B. , vol.55 , pp. 3-23
    • Smith, A.F.M.1    Roberts, G.O.2
  • 25
    • 84950758368 scopus 로고
    • The calculation of posterior distributions by data augmentation. J
    • Tanner, M.A. and Wong, W.H. (1987) The calculation of posterior distributions by data augmentation. J. Amer. Statist. Assoc., 82, 528-540.
    • (1987) Amer. Statist. Assoc. , vol.82 , pp. 528-540
    • Tanner, M.A.1    Wong, W.H.2
  • 26
    • 0000576595 scopus 로고
    • Markov chains for exploring posterior distributions (with discussion)
    • Tierney, L. (1994) Markov chains for exploring posterior distributions (with discussion). Ann. Statist., 22, 1701-1762.
    • (1994) Ann. Statist. , vol.22 , pp. 1701-1762
    • Tierney, L.1
  • 27
    • 0001560641 scopus 로고
    • Fully exponential Laplace approximations to expectations and variances of nonpositive functions
    • Tiemey, L., Kass, R.E. and Kadane, J.B. (1989) Fully exponential Laplace approximations to expectations and variances of nonpositive functions. J. Amer. Statist. Assoc., 84, 710-716.
    • (1989) J. Amer. Statist. Assoc. , vol.84 , pp. 710-716
    • Tiemey, L.1    Kass, R.E.2    Kadane, J.B.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.