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Volumn 16, Issue 3, 2010, Pages 882-902

Quantitative bounds for Markov chain convergence: Wasserstein and total variation distances

Author keywords

Convergence rate; Coupling; Gibbs sampler; Iterated random functions; Local contractivity; Logistic map; Markov chain; Random dynamical system; Total variation distance; Wasserstein distance

Indexed keywords


EID: 77957564940     PISSN: 13507265     EISSN: None     Source Type: Journal    
DOI: 10.3150/09-BEJ238     Document Type: Article
Times cited : (59)

References (23)
  • 1
    • 0003158042 scopus 로고
    • A new class of Markov processes for image encoding
    • MR0932532
    • Barnsley, M. F. and Elton, J. H. (1988). A new class of Markov processes for image encoding. Adv. in Appl. Probab. 20 14-32. MR0932532
    • (1988) Adv. in Appl. Probab. , vol.20 , pp. 14-32
    • Barnsley, M.F.1    Elton, J.H.2
  • 2
    • 28944449679 scopus 로고    scopus 로고
    • One-shot CFTP: Application to a class of truncated Gaussian densities
    • MR2235153
    • Beskos, A. and Roberts, G. O. (2005). One-shot CFTP: Application to a class of truncated Gaussian densities. Methodol. Comput. Appl. Probab. 7 407-437. MR2235153
    • (2005) Methodol. Comput. Appl. Probab. , vol.7 , pp. 407-437
    • Beskos, A.1    Roberts, G.O.2
  • 3
    • 0002370188 scopus 로고
    • Explicit stationary distributions for compositions of random functions and random matrices
    • MR1088391
    • Chamayou, J.-F. and Letac, G. (1991). Explicit stationary distributions for compositions of random functions and random matrices. J. Theoret. Probab. 4 3-36. MR1088391
    • (1991) J. Theoret. Probab. , vol.4 , pp. 3-36
    • Chamayou, J.-F.1    Letac, G.2
  • 6
    • 0002284829 scopus 로고    scopus 로고
    • Iterated random functions
    • MR1669737
    • Diaconis, P. and Freedman, D. (1999). Iterated random functions. SIAM Rev. 41 45-76. MR1669737
    • (1999) SIAM Rev. , vol.41 , pp. 45-76
    • Diaconis, P.1    Freedman, D.2
  • 8
    • 8644241717 scopus 로고    scopus 로고
    • Convergence in the Wasserstein metric for Markov chain Monte Carlo algorithms with applications to image restoration
    • MR2094049
    • Gibbs, A. L. (2004). Convergence in the Wasserstein metric for Markov chain Monte Carlo algorithms with applications to image restoration. Stoch. Models 20 473-492. MR2094049
    • (2004) Stoch. Models , vol.20 , pp. 473-492
    • Gibbs, A.L.1
  • 9
    • 0036896227 scopus 로고    scopus 로고
    • On choosing and bounding probability metrics
    • Gibbs, A. L. and Su, F. E. (2002). On choosing and bounding probability metrics. Internat. Statist. Rev. 70 419-435.
    • (2002) Internat. Statist. Rev. , vol.70 , pp. 419-435
    • Gibbs, A.L.1    Su, F.E.2
  • 10
    • 0003860037 scopus 로고    scopus 로고
    • Gilks, W. R., Richardson, S. and Spiegelhalter, D. J., eds, London: Chapman and Hall. MR1397966
    • Gilks, W. R., Richardson, S. and Spiegelhalter, D. J., eds. (1996). Markov Chain Monte Carlo in Practice. London: Chapman and Hall. MR1397966
    • (1996) Markov Chain Monte Carlo in Practice
  • 11
    • 0038569359 scopus 로고    scopus 로고
    • Geometric ergodicity of Gibbs and block Gibbs samplers for a hierarchical random effects model
    • MR1659196
    • Hobert, J. P. and Geyer, C. J. (1998). Geometric ergodicity of Gibbs and block Gibbs samplers for a hierarchical random effects model. J. Multivariate Anal. 67 414-430. MR1659196
    • (1998) J. Multivariate Anal. , vol.67 , pp. 414-430
    • Hobert, J.P.1    Geyer, C.J.2
  • 12
    • 34547459727 scopus 로고    scopus 로고
    • Perfect simulation for image restoration
    • MR2341079
    • Huber, M. (2007). Perfect simulation for image restoration. Stoch. Models 23 475-487. MR2341079
    • (2007) Stoch. Models , vol.23 , pp. 475-487
    • Huber, M.1
  • 13
    • 0000002644 scopus 로고    scopus 로고
    • Mathematical foundations of the Monte Carlo method
    • M. Habib et al., eds., Berlin: Springer. MR1678570
    • Jerrum, M. (1998). Mathematical foundations of the Monte Carlo method. In Probabilistic Methods for Algorithmic Discrete Mathematics (M. Habib et al., eds.) 116-165. Berlin: Springer. MR1678570
    • (1998) Probabilistic Methods for Algorithmic Discrete Mathematics , pp. 116-165
    • Jerrum, M.1
  • 14
    • 0000154395 scopus 로고    scopus 로고
    • Honest exploration of intractable probability distributions via Markov chain Monte Carlo
    • MR1888447
    • Jones, G. L. and Hobert, J. P. (2001). Honest exploration of intractable probability distributions via Markov chain Monte Carlo. Statist. Sci. 16 312-334. MR1888447
    • (2001) Statist. Sci. , vol.16 , pp. 312-334
    • Jones, G.L.1    Hobert, J.P.2
  • 17
    • 0002074149 scopus 로고    scopus 로고
    • Geometric ergodicity and hybrid Markov chains
    • electronic. MR1448322
    • Roberts, G. O. and Rosenthal, J. S. (1997). Geometric ergodicity and hybrid Markov chains. Electron. Comm. Probab. 2 13-25 (electronic). MR1448322
    • (1997) Electron. Comm. Probab. , vol.2 , pp. 13-25
    • Roberts, G.O.1    Rosenthal, J.S.2
  • 18
    • 0036237412 scopus 로고    scopus 로고
    • One-shot coupling for certain stochastic recursive sequences
    • MR1901153
    • Roberts, G. O. and Rosenthal, J. S. (2002). One-shot coupling for certain stochastic recursive sequences. Stochastic Process. Appl. 99 195-208. MR1901153
    • (2002) Stochastic Process. Appl. , vol.99 , pp. 195-208
    • Roberts, G.O.1    Rosenthal, J.S.2
  • 19
    • 84890736685 scopus 로고    scopus 로고
    • General state space Markov chains and MCMC algorithms
    • electronic. MR2095565
    • Roberts, G. O. and Rosenthal, J. S. (2004). General state space Markov chains and MCMC algorithms. Probab. Surv. 1 20-71 (electronic). MR2095565
    • (2004) Probab. Surv , vol.1 , pp. 20-71
    • Roberts, G.O.1    Rosenthal, J.S.2
  • 20
    • 84923618271 scopus 로고
    • Minorization conditions and convergence rates for Markov chain Monte Carlo
    • MR1340509
    • Rosenthal, J. S. (1995). Minorization conditions and convergence rates for Markov chain Monte Carlo. J. Amer. Stat. Assoc. 90 558-566. MR1340509
    • (1995) J. Amer. Stat. Assoc. , vol.90 , pp. 558-566
    • Rosenthal, J.S.1
  • 22
    • 0033233682 scopus 로고    scopus 로고
    • Locally contractive iterated function systems
    • MR1742896
    • Steinsaltz, D. (1999). Locally contractive iterated function systems. Ann. Probab. 27 1952-1979. MR1742896
    • (1999) Ann. Probab. , vol.27 , pp. 1952-1979
    • Steinsaltz, D.1
  • 23
    • 0035905154 scopus 로고    scopus 로고
    • Random logistic maps and Lyapunov exponents
    • MR1908881
    • Steinsaltz, D. (2001). Random logistic maps and Lyapunov exponents. Indag. Math. (N. S.) 12 557-584. MR1908881
    • (2001) Indag. Math. (N. S.) , vol.12 , pp. 557-584
    • Steinsaltz, D.1


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