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Volumn 40, Issue 6, 2012, Pages 3050-3076

Variable transformation to obtain geometric ergodicity in the random-walk Metropolis algorithm

Author keywords

Change of variable; Conjugate prior; Drift condition; Exponential family; Markov chain isomorphism; Markov chain Monte Carlo; Metropolis Hastings Green algorithm

Indexed keywords


EID: 84879185383     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/12-AOS1048     Document Type: Article
Times cited : (49)

References (47)
  • 3
    • 38249002416 scopus 로고
    • On the central limit theorem for an ergodic Markov chain
    • MR1232855
    • CHAN, K. S. (1993). On the central limit theorem for an ergodic Markov chain. Stochastic Process. Appl. 47 113-117. MR1232855
    • (1993) Stochastic Process. Appl. , vol.47 , pp. 113-117
    • Chan, K.S.1
  • 4
    • 0000576596 scopus 로고
    • Comment on "markov chains for exploring posterior distributions."
    • CHAN, K. S. and GEYER, C. J. (1994). Comment on "Markov chains for exploring posterior distributions." Ann. Statist. 22 1747-1758.
    • (1994) Ann. Statist. , vol.22 , pp. 1747-1758
    • Chan, K.S.1    Geyer, C.J.2
  • 5
    • 0000811835 scopus 로고
    • Conjugate priors for exponential families
    • MR0520238
    • DIACONIS, P. and YLVISAKER, D. (1979). Conjugate priors for exponential families. Ann. Statist. 7 269-281. MR0520238
    • (1979) Ann. Statist. , vol.7 , pp. 269-281
    • Diaconis, P.1    Ylvisaker, D.2
  • 6
    • 77649301784 scopus 로고    scopus 로고
    • Batch means and spectral variance estimators in Markov chain Monte Carlo
    • MR2604704
    • FLEGAL, J. M. and JONES, G. L. (2010). Batch means and spectral variance estimators in Markov chain Monte Carlo. Ann. Statist. 38 1034-1070. MR2604704
    • (2010) Ann. Statist. , vol.38 , pp. 1034-1070
    • Flegal, J.M.1    Jones, G.L.2
  • 7
    • 84950453304 scopus 로고
    • Sampling-based approaches to calculating marginal densities
    • MR1141740
    • GELFAND, A. E. and SMITH, A. F. M. (1990). Sampling-based approaches to calculating marginal densities. J. Amer. Statist. Assoc. 85 398-409. MR1141740
    • (1990) J. Amer. Statist. Assoc. , vol.85 , pp. 398-409
    • Gelfand, A.E.1    Smith, A.F.M.2
  • 8
    • 0021518209 scopus 로고
    • Stochastic relaxtion, Gibbs distributions, and the Bayesian restoration of images
    • GEMAN, S. and GEMAN, D. (1984). Stochastic relaxtion, Gibbs distributions, and the Bayesian restoration of images. IEEE Trans. Pattern Anal. Mach. Intell. 6 721-741.
    • (1984) IEEE Trans. Pattern Anal. Mach. Intell. , vol.6 , pp. 721-741
    • Geman, S.1    Geman, D.2
  • 9
    • 84972511893 scopus 로고
    • Practical Markov chainMonte Carlo (with discussion)
    • GEYER, C. J. (1992). Practical Markov chainMonte Carlo (with discussion). Statist. Sci. 7 473-511.
    • (1992) Statist. Sci. , vol.7 , pp. 473-511
    • Geyer, C.J.1
  • 10
    • 84862504558 scopus 로고    scopus 로고
    • Introduction to MCMC
    • (S. P. Brooks, A. E. Gelman, G. L. Jones and X. L. Meng, eds.). Chapman & Hall/CRC, Boca Raton
    • GEYER, C. J. (2011). Introduction to MCMC. In Handbook of Markov Chain Monte Carlo (S. P. Brooks, A. E. Gelman, G. L. Jones and X. L. Meng, eds.). Chapman & Hall/CRC, Boca Raton.
    • (2011) Handbook of Markov Chain Monte Carlo
    • Geyer, C.J.1
  • 12
    • 0001309227 scopus 로고
    • Simulation procedures and likelihood inference for spatial point processes
    • MR1310082
    • GEYER, C. J. and MØLLER, J. (1994). Simulation procedures and likelihood inference for spatial point processes. Scand. J. Stat. 21 359-373. MR1310082
    • (1994) Scand. J. Stat. , vol.21 , pp. 359-373
    • Geyer, C.J.1    MØller, J.2
  • 14
    • 0002359079 scopus 로고
    • Central limit theorem for stationary Markov processes
    • MR0501277
    • GORDIN, M. I. and LIFŠIC, B. A. (1978). Central limit theorem for stationary Markov processes. Dokl. Akad. Nauk SSSR 239 766-767. MR0501277
    • (1978) Dokl. Akad. Nauk SSSR , vol.239 , pp. 766-767
    • Gordin, M.I.1    Lifšic, B.A.2
  • 15
    • 77956889087 scopus 로고
    • Reversible jump Markov chain Monte Carlo computation and Bayesian model determination
    • MR1380810
    • GREEN, P. J. (1995). Reversible jump Markov chain Monte Carlo computation and Bayesian model determination. Biometrika 82 711-732. MR1380810
    • (1995) Biometrika , vol.82 , pp. 711-732
    • Green, P.J.1
  • 17
    • 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
  • 18
    • 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
  • 19
    • 0001562199 scopus 로고    scopus 로고
    • Geometric ergodicity of Metropolis algorithms
    • MR1731030
    • JARNER, S. F. and HANSEN, E. (2000). Geometric ergodicity of Metropolis algorithms. Stochastic Process. Appl. 85 341-361. MR1731030
    • (2000) Stochastic Process. Appl. , vol.85 , pp. 341-361
    • Jarner, S.F.1    Hansen, E.2
  • 20
    • 0036117479 scopus 로고    scopus 로고
    • Polynomial convergence rates of Markov chains
    • MR1890063
    • JARNER, S. F. and ROBERTS, G. O. (2002). Polynomial convergence rates of Markov chains. Ann. Appl. Probab. 12 224-247. MR1890063
    • (2002) Ann. Appl. Probab. , vol.12 , pp. 224-247
    • Jarner, S.F.1    Roberts, G.O.2
  • 21
    • 36749103743 scopus 로고    scopus 로고
    • Convergence of heavy-tailed Monte Carlo Markov chain algorithms
    • MR2396939
    • JARNER, S. F. and ROBERTS, G. O. (2007). Convergence of heavy-tailed Monte Carlo Markov chain algorithms. Scand. J. Stat. 34 781-815. MR2396939
    • (2007) Scand. J. Stat. , vol.34 , pp. 781-815
    • Jarner, S.F.1    Roberts, G.O.2
  • 22
    • 33747336738 scopus 로고    scopus 로고
    • Necessary conditions for geometric and polynomial ergodicity of random-walk-type Markov chains
    • MR1996270
    • JARNER, S. F. and TWEEDIE, R. L. (2003). Necessary conditions for geometric and polynomial ergodicity of random-walk-type Markov chains. Bernoulli 9 559-578. MR1996270
    • (2003) Bernoulli , vol.9 , pp. 559-578
    • Jarner, S.F.1    Tweedie, R.L.2
  • 23
    • 78649758959 scopus 로고    scopus 로고
    • Gibbs sampling for a Bayesian hierarchical general linear model
    • MR2645487
    • JOHNSON, A. A. and JONES, G. L. (2010). Gibbs sampling for a Bayesian hierarchical general linear model. Electron. J. Stat. 4 313-333. MR2645487
    • (2010) Electron. J. Stat. , vol.4 , pp. 313-333
    • Johnson, A.A.1    Jones, G.L.2
  • 24
    • 33645087459 scopus 로고    scopus 로고
    • On the Markov chain central limit theorem
    • MR2068475
    • JONES, G. L. (2004). On the Markov chain central limit theorem. Probab. Surv. 1 299-320. MR2068475
    • (2004) Probab. Surv. , vol.1 , pp. 299-320
    • Jones, G.L.1
  • 25
    • 24344493048 scopus 로고    scopus 로고
    • Sufficient burn-in for Gibbs samplers for a hierarchical random effects model
    • MR2060178
    • JONES, G. L. and HOBERT, J. P. (2004). Sufficient burn-in for Gibbs samplers for a hierarchical random effects model. Ann. Statist. 32 784-817. MR2060178
    • (2004) Ann. Statist. , vol.32 , pp. 784-817
    • Jones, G.L.1    Hobert, J.P.2
  • 26
    • 34250130646 scopus 로고
    • Central limit theorem for additive functionals of reversible Markov processes and applications to simple exclusions
    • MR0834478
    • KIPNIS, C. and VARADHAN, S. R. S. (1986). Central limit theorem for additive functionals of reversible Markov processes and applications to simple exclusions. Comm. Math. Phys. 104 1-19. MR0834478
    • (1986) Comm. Math. Phys. , vol.104 , pp. 1-19
    • Kipnis, C.1    Varadhan, S.R.S.2
  • 27
    • 84879182156 scopus 로고    scopus 로고
    • Nonasymptotic bounds on the estimation error of MCMC algorithms
    • To appear
    • ŁATUSZYŃSKI, K., MIASOJEDOW, B. and NIEMIRO, W. (2012). Nonasymptotic bounds on the estimation error of MCMC algorithms. Bernoulli. To appear.
    • (2012) Bernoulli
    • Łatuszyński, K.1    Miasojedow, B.2    Niemiro, W.3
  • 28
    • 78649724375 scopus 로고    scopus 로고
    • Rigorous confidence bounds for MCMC under a geometric drift condition
    • MR2745298
    • ŁATUSZYŃSKI, K. and NIEMIRO, W. (2011). Rigorous confidence bounds for MCMC under a geometric drift condition. J. Complexity 27 23-38. MR2745298
    • (2011) J. Complexity , vol.27 , pp. 23-38
    • Łatuszyński, K.1    Niemiro, W.2
  • 29
    • 0001583850 scopus 로고
    • Théorè;me de limite centrale fonctionnel pour une chaîne de Markov récurrente au sens de Harris et positive
    • MR0523221
    • MAIGRET, N. (1978). Théorè;me de limite centrale fonctionnel pour une chaîne de Markov récurrente au sens de Harris et positive. Ann. Inst. H. Poincaré Sect. B (N.S.) 14 425-440. MR0523221
    • (1978) Ann. Inst. H. Poincaré Sect. B (N.S.) , vol.14 , pp. 425-440
    • Maigret, N.1
  • 30
    • 0030551974 scopus 로고    scopus 로고
    • Rates of convergence of the Hastings and Metropolis algorithms
    • MR1389882
    • MENGERSEN, K. L. and TWEEDIE, R. L. (1996). Rates of convergence of the Hastings and Metropolis algorithms. Ann. Statist. 24 101-121. MR1389882
    • (1996) Ann. Statist. , vol.24 , pp. 101-121
    • Mengersen, K.L.1    Tweedie, R.L.2
  • 33
    • 0003209629 scopus 로고
    • General irreducible Markov chains and nonnegative operators
    • Cambridge Univ. Press, Cambridge. MR0776608
    • NUMMELIN, E. (1984). General Irreducible Markov Chains and Nonnegative Operators. Cambridge Tracts in Mathematics 83. Cambridge Univ. Press, Cambridge. MR0776608
    • (1984) Cambridge Tracts in Mathematics , vol.83
    • Nummelin, E.1
  • 34
    • 34249101736 scopus 로고    scopus 로고
    • A general framework for the parametrization of hierarchical models
    • MR2408661
    • PAPASPILIOPOULOS, O., ROBERTS, G. O. and SKÖLD, M. (2007). A general framework for the parametrization of hierarchical models. Statist. Sci. 22 59-73. MR2408661
    • (2007) Statist. Sci. , vol.22 , pp. 59-73
    • Papaspiliopoulos, O.1    Roberts, G.O.2    Sköld, M.3
  • 35
    • 50649109863 scopus 로고    scopus 로고
    • Stability of the Gibbs sampler for Bayesian hierarchical models
    • MR2387965
    • PAPASPILIOPOULOS, O. and ROBERTS, G. (2008). Stability of the Gibbs sampler for Bayesian hierarchical models. Ann. Statist. 36 95-117. MR2387965
    • (2008) Ann. Statist. , vol.36 , pp. 95-117
    • Papaspiliopoulos, O.1    Roberts, G.2
  • 36
    • 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. Commun. Probab. 2 13-25 (electronic). MR1448322
    • (1997) Electron. Commun. Probab. , vol.2 , pp. 13-25
    • Roberts, G.O.1    Rosenthal, J.S.2
  • 37
    • 84890736685 scopus 로고    scopus 로고
    • General state space Markov chains and MCMC algorithms
    • MR2095565
    • ROBERTS, G. O. and ROSENTHAL, J. S. (2004). General state space Markov chains and MCMC algorithms. Probab. Surv. 1 20-71. MR2095565
    • (2004) Probab. Surv. , vol.1 , pp. 20-71
    • Roberts, G.O.1    Rosenthal, J.S.2
  • 38
    • 0000051645 scopus 로고    scopus 로고
    • Updating schemes, correlation structure, blocking and parameterization for the Gibbs sampler
    • MR1440584
    • ROBERTS, G. O. and SAHU, S. K. (1997). Updating schemes, correlation structure, blocking and parameterization for the Gibbs sampler. J. Roy. Statist. Soc. Ser. B 59 291-317. MR1440584
    • (1997) J. Roy. Statist. Soc. Ser. B , vol.59 , pp. 291-317
    • Roberts, G.O.1    Sahu, S.K.2
  • 39
    • 33746388444 scopus 로고    scopus 로고
    • Geometric convergence and central limit theorems for multidimensional Hastings and Metropolis algorithms
    • MR1399158
    • ROBERTS, G. O. and TWEEDIE, R. L. (1996). Geometric convergence and central limit theorems for multidimensional Hastings and Metropolis algorithms. Biometrika 83 95-110. MR1399158
    • (1996) Biometrika , vol.83 , pp. 95-110
    • Roberts, G.O.1    Tweedie, R.L.2
  • 41
    • 21444459448 scopus 로고
    • Analysis of the Gibbs sampler for a model related to James-Stein estimators. Stat
    • ROSENTHAL, J. S. (1995a). Analysis of the Gibbs sampler for a model related to James-Stein estimators. Stat. Comput. 6 269-275.
    • (1995) Comput. , vol.6 , pp. 269-275
    • Rosenthal, J.S.1
  • 42
    • 84923618271 scopus 로고
    • Minorization conditions and convergence rates for Markov chainMonte Carlo
    • MR1340509
    • ROSENTHAL, J. S. (1995b).Minorization conditions and convergence rates for Markov chainMonte Carlo. J. Amer. Statist. Assoc. 90 558-566. MR1340509
    • (1995) J. Amer. Statist. Assoc. , vol.90 , pp. 558-566
    • Rosenthal, J.S.1
  • 43
    • 34547837457 scopus 로고    scopus 로고
    • Convergence rates and asymptotic standard errors for Markov chain Monte Carlo algorithms for Bayesian probit regression
    • MR2370071
    • ROY, V. and HOBERT, J. P. (2007). Convergence rates and asymptotic standard errors for Markov chain Monte Carlo algorithms for Bayesian probit regression. J. R. Stat. Soc. Ser. B Stat. Methodol. 69 607-623. MR2370071
    • (2007) J. R. Stat. Soc. Ser. B Stat. Methodol. , vol.69 , pp. 607-623
    • Roy, V.1    Hobert, J.P.2
  • 45
    • 72449129941 scopus 로고    scopus 로고
    • Block Gibbs sampling for Bayesian random effects models with improper priors: Convergence and regeneration
    • MR2598033
    • TAN, A. and HOBERT, J. P. (2009). Block Gibbs sampling for Bayesian random effects models with improper priors: Convergence and regeneration. J. Comput. Graph. Statist. 18 861-878. MR2598033
    • (2009) J. Comput. Graph. Statist. , vol.18 , pp. 861-878
    • Tan, A.1    Hobert, J.P.2
  • 46
    • 84950758368 scopus 로고
    • The calculation of posterior distributions by data augmentation
    • MR0898357
    • TANNER, M. A. and WONG, W. H. (1987). The calculation of posterior distributions by data augmentation. J. Amer. Statist. Assoc. 82 528-550. MR0898357
    • (1987) J. Amer. Statist. Assoc. , vol.82 , pp. 528-550
    • Tanner, M.A.1    Wong, W.H.2
  • 47
    • 0000576595 scopus 로고
    • Markov chains for exploring posterior distributions
    • MR1329166
    • TIERNEY, L. (1994). Markov chains for exploring posterior distributions. Ann. Statist. 22 1701-1762. MR1329166
    • (1994) Ann. Statist. , vol.22 , pp. 1701-1762
    • Tierney, L.1


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