메뉴 건너뛰기




Volumn 33, Issue 1, 2006, Pages 37-51

Using a Markov chain to construct a tractable approximation of an intractable probability distribution

Author keywords

Burn in; Gibbs sampler; Minorization condition; Mixture representation; Monte Carlo; Regeneration; Split chain

Indexed keywords


EID: 33645047932     PISSN: 03036898     EISSN: 14679469     Source Type: Journal    
DOI: 10.1111/j.1467-9469.2006.00467.x     Document Type: Article
Times cited : (9)

References (40)
  • 2
    • 0000991156 scopus 로고
    • A new approach to the limit theory of recurrent Markov chains
    • Athreya, K. B. & Ney, P. (1978). A new approach to the limit theory of recurrent Markov chains. Trans. Am. Math. Soc. 245, 493-501.
    • (1978) Trans. Am. Math. Soc. , vol.245 , pp. 493-501
    • Athreya, K.B.1    Ney, P.2
  • 3
    • 14544277112 scopus 로고    scopus 로고
    • Renewal theory and computable convergence rates for geometrically ergodic Markov chains
    • Baxendale, P. H. (2005). Renewal theory and computable convergence rates for geometrically ergodic Markov chains. Ann. Appl. Probab. 15, 700-738.
    • (2005) Ann. Appl. Probab. , vol.15 , pp. 700-738
    • Baxendale, P.H.1
  • 5
    • 20744442841 scopus 로고    scopus 로고
    • Identification of regeneration times in MCMC simulation, with application to adaptive schemes
    • Brockwell, A. E. & Kadane, J. B. (2005). Identification of regeneration times in MCMC simulation, with application to adaptive schemes. J. Comput. Graph. Statist. 14, 436-458.
    • (2005) J. Comput. Graph. Statist. , vol.14 , pp. 436-458
    • Brockwell, A.E.1    Kadane, J.B.2
  • 6
    • 0041481053 scopus 로고    scopus 로고
    • Perfect forward simulation via simulated tempering
    • University of Cambridge, Cambridge
    • Brooks, S. P., Fan, Y. & Rosenthal, J. S. (2004). Perfect forward simulation via simulated tempering. Technical Report, University of Cambridge, Cambridge.
    • (2004) Technical Report
    • Brooks, S.P.1    Fan, Y.2    Rosenthal, J.S.3
  • 7
    • 0033468528 scopus 로고    scopus 로고
    • Central limit theorems for the Wasserstein distance between the empirical and the true distributions
    • Del Barrio, E., Gine, E. & Matran, C. (1999). Central limit theorems for the Wasserstein distance between the empirical and the true distributions. Ann. Probab. 27, 1009-1071.
    • (1999) Ann. Probab. , vol.27 , pp. 1009-1071
    • Del Barrio, E.1    Gine, E.2    Matran, C.3
  • 8
    • 14544282666 scopus 로고    scopus 로고
    • Quantitative bounds on convergence of timeinhomogeneous Markov chains
    • Douc, R., Moulines, E. & Rosenthal, J. S. (2004). Quantitative bounds on convergence of timeinhomogeneous Markov chains. Ann. Appl. Probab. 14, 1643-1665.
    • (2004) Ann. Appl. Probab. , vol.14 , pp. 1643-1665
    • Douc, R.1    Moulines, E.2    Rosenthal, J.S.3
  • 9
    • 0034360070 scopus 로고    scopus 로고
    • Extension of Fill's perfect rejection sampling algorithm to general chains
    • Fill, J. A., Machida, M., Murdoch, D. J. & Rosenthal, J. S. (2000). Extension of Fill's perfect rejection sampling algorithm to general chains. Random Struc. Algorithms 17, 290-316.
    • (2000) Random Struc. Algorithms , vol.17 , pp. 290-316
    • Fill, J.A.1    Machida, M.2    Murdoch, D.J.3    Rosenthal, J.S.4
  • 10
    • 84972492387 scopus 로고
    • Inference from iterative simulation using multiple sequences (with discussion)
    • Gelman, A. & Rubin, D. B. (1992). Inference from iterative simulation using multiple sequences (with discussion). Statist. Sci. 7, 457-472.
    • (1992) Statist. Sci. , vol.7 , pp. 457-472
    • Gelman, A.1    Rubin, D.B.2
  • 11
    • 0000106855 scopus 로고
    • On the convergence of Monte Carlo maximum likelihood calculations
    • Geyer, C. J. (1994). On the convergence of Monte Carlo maximum likelihood calculations. J. Roy. Statist. Soc. Ser. B 56, 261-274.
    • (1994) J. Roy. Statist. Soc. Ser. B , vol.56 , pp. 261-274
    • Geyer, C.J.1
  • 12
    • 0000247137 scopus 로고    scopus 로고
    • Estimation and optimization of functions
    • (eds W. R. Gilks, S. Richardson & D. J. E. Spiegelhalter), Chapman & Hall, Boca Raton
    • Geyer, C. J. (1996). Estimation and optimization of functions. In Markov chain Monte Carlo in practice (eds W. R. Gilks, S. Richardson & D. J. E. Spiegelhalter), 241-258. Chapman & Hall, Boca Raton.
    • (1996) Markov Chain Monte Carlo in Practice , pp. 241-258
    • Geyer, C.J.1
  • 13
    • 84950437936 scopus 로고
    • Annealing Markov chain Monte Carlo with applications to ancestral inference
    • Geyer, C. J. & Thompson, E. A. (1995). Annealing Markov chain Monte Carlo with applications to ancestral inference. J. Am. Statist. Assoc. 90, 909-920.
    • (1995) J. Am. Statist. Assoc. , vol.90 , pp. 909-920
    • Geyer, C.J.1    Thompson, E.A.2
  • 14
    • 0035351618 scopus 로고    scopus 로고
    • Computing densities for Markov chains via simulation
    • Henderson, S. G. & Glynn, P. W. (2001). Computing densities for Markov chains via simulation. Math. Oper. Res. 26, 375-400.
    • (2001) Math. Oper. Res. , vol.26 , pp. 375-400
    • Henderson, S.G.1    Glynn, P.W.2
  • 15
    • 0038569359 scopus 로고    scopus 로고
    • Geometric ergodicity of Gibbs and block Gibbs samplers for a hierarchical random effects model
    • Hobert, J. P. & Geyer, C. J. (1998). Geometric ergodicity of Gibbs and block Gibbs samplers for a hierarchical random effects model. J. Multivar. Anal. 67, 414-430.
    • (1998) J. Multivar. Anal. , vol.67 , pp. 414-430
    • Hobert, J.P.1    Geyer, C.J.2
  • 16
    • 9744242175 scopus 로고    scopus 로고
    • A mixture representation of π with applications in Markov chain Monte Carlo and perfect sampling
    • Hobert, J. P. & Robert, C. P. (2004). A mixture representation of π with applications in Markov chain Monte Carlo and perfect sampling. Ann. Appl. Probab. 14, 1295-1305.
    • (2004) Ann. Appl. Probab. , vol.14 , pp. 1295-1305
    • Hobert, J.P.1    Robert, C.P.2
  • 17
    • 2142780945 scopus 로고    scopus 로고
    • On the applicability of regenerative simulation in Markov chain Monte Carlo
    • Hobert, J. P., Jones, G. L., Presnell, B. & Rosenthal, J. S. (2002). On the applicability of regenerative simulation in Markov chain Monte Carlo. Biometrika 89, 731-743.
    • (2002) Biometrika , vol.89 , pp. 731-743
    • Hobert, J.P.1    Jones, G.L.2    Presnell, B.3    Rosenthal, J.S.4
  • 18
    • 0036117479 scopus 로고    scopus 로고
    • Polynomial convergence rates of Markov chains
    • Jarner, S. F. & Roberts, G. O. (2002). Polynomial convergence rates of Markov chains. Ann. Appl. Probab. 12, 224-247.
    • (2002) Ann. Appl. Probab. , vol.12 , pp. 224-247
    • Jarner, S.F.1    Roberts, G.O.2
  • 19
    • 33645087459 scopus 로고    scopus 로고
    • On the Markov chain central limit theorem
    • Jones, G. L. (2004). On the Markov chain central limit theorem. Probab. Surveys 1, 299-320.
    • (2004) Probab. Surveys , vol.1 , pp. 299-320
    • Jones, G.L.1
  • 20
    • 0000154395 scopus 로고    scopus 로고
    • Honest exploration of intractable probability distributions via Markov chain Monte Carlo
    • Jones, G. L. & Hobert, J. P. (2001). Honest exploration of intractable probability distributions via Markov chain Monte Carlo. Statist. Sci. 16, 312-334.
    • (2001) Statist. Sci. , vol.16 , pp. 312-334
    • Jones, G.L.1    Hobert, J.P.2
  • 21
    • 24344493048 scopus 로고    scopus 로고
    • Sufficient burn-in for Gibbs samplers for a hierarchical random effects model
    • Jones, G. L. & Hobert, J. P. (2004). Sufficient burn-in for Gibbs samplers for a hierarchical random effects model. Ann. Statist. 32, 784-817.
    • (2004) Ann. Statist. , vol.32 , pp. 784-817
    • Jones, G.L.1    Hobert, J.P.2
  • 23
    • 33644899039 scopus 로고
    • Simulated tempering: A new Monte Carlo scheme
    • Marinari, E. & Parisi, G. (1992). Simulated tempering: A new Monte Carlo scheme. Europhys. Lett. 19, 451-458.
    • (1992) Europhys. Lett. , vol.19 , pp. 451-458
    • Marinari, E.1    Parisi, G.2
  • 24
    • 0030551974 scopus 로고    scopus 로고
    • Rates of convergence of the Hastings and Metropolis algorithms
    • Mengersen, K. & Tweedie, R. L. (1996). Rates of convergence of the Hastings and Metropolis algorithms. Ann. Statist. 24, 101-121.
    • (1996) Ann. Statist. , vol.24 , pp. 101-121
    • Mengersen, K.1    Tweedie, R.L.2
  • 26
    • 0000566364 scopus 로고
    • Computable bounds for geometric convergence rates of Markov chains
    • Meyn, S. P. & Tweedie, R. L. (1994). Computable bounds for geometric convergence rates of Markov chains. Ann. Appl. Probab. 4, 981-1011.
    • (1994) Ann. Appl. Probab. , vol.4 , pp. 981-1011
    • Meyn, S.P.1    Tweedie, R.L.2
  • 27
    • 84858562613 scopus 로고    scopus 로고
    • Perfect simulation for sample-based inference
    • forthcoming
    • Möller, J. & Nicholls, G. K. (2005). Perfect simulation for sample-based inference. Stat. Comput., forthcoming.
    • (2005) Stat. Comput.
    • Möller, J.1    Nicholls, G.K.2
  • 28
    • 0032363044 scopus 로고    scopus 로고
    • Exact sampling from a continuous state space
    • Murdoch, D. J. & Green, P. J. (1998). Exact sampling from a continuous state space. Scand. J. Statist. 25, 483-502.
    • (1998) Scand. J. Statist. , vol.25 , pp. 483-502
    • Murdoch, D.J.1    Green, P.J.2
  • 30
    • 0000427555 scopus 로고
    • A splitting technique for Harris recurrent Markov chains
    • Nummelin, E. (1978). A splitting technique for Harris recurrent Markov chains. Z. Wahr. Verw. Geb. 43, 309-318.
    • (1978) Z. Wahr. Verw. Geb. , vol.43 , pp. 309-318
    • Nummelin, E.1
  • 32
    • 1842607847 scopus 로고    scopus 로고
    • R Foundation for Statistical Computing, Vienna, Austria. ISBN 3-900051-00-3
    • R Development Core Team (2004). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. ISBN 3-900051-00-3.
    • (2004) R: A Language and Environment for Statistical Computing
  • 34
    • 0001514831 scopus 로고    scopus 로고
    • Bounds on regeneration times and convergence rates for Markov chains
    • Roberts, G. O. & Tweedie, R. L. (1999). Bounds on regeneration times and convergence rates for Markov chains. Stochast. Process. Appl. 80, 211-229.
    • (1999) Stochast. Process. Appl. , vol.80 , pp. 211-229
    • Roberts, G.O.1    Tweedie, R.L.2
  • 35
    • 84923618271 scopus 로고
    • Minorization conditions and convergence rates for Markov chain Monte Carlo
    • Rosenthal, J. S. (1995a). Minorization conditions and convergence rates for Markov chain Monte Carlo. J. Am. Statist. Assoc. 90, 558-566.
    • (1995) J. Am. Statist. Assoc. , vol.90 , pp. 558-566
    • Rosenthal, J.S.1
  • 36
    • 0001096889 scopus 로고
    • Rates of convergence for Gibbs sampling for variance component models
    • Rosenthal, J. S. (1995b). Rates of convergence for Gibbs sampling for variance component models. Ann. Statist. 23, 740-761.
    • (1995) Ann. Statist. , vol.23 , pp. 740-761
    • Rosenthal, J.S.1
  • 39
    • 0242458502 scopus 로고    scopus 로고
    • Density estimation for the Metropolis-Hastings algorithm
    • Sköld, M. & Roberts, G. O. (2003). Density estimation for the Metropolis-Hastings algorithm. Scand. J. Statist. 31, 699-718.
    • (2003) Scand. J. Statist. , vol.31 , pp. 699-718
    • Sköld, M.1    Roberts, G.O.2
  • 40
    • 0034381555 scopus 로고    scopus 로고
    • How to couple from the past using a read-once source of randomness
    • Wilson, D. B. (2000). How to couple from the past using a read-once source of randomness. Random Struct. Algorithms 16, 85-113.
    • (2000) Random Struct. Algorithms , vol.16 , pp. 85-113
    • Wilson, D.B.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.