메뉴 건너뛰기




Volumn 15, Issue 1 B, 2005, Pages 700-738

Renewal theory and computable convergence rates for geometrically ergodic Markov chains

Author keywords

Geometric ergodicity; Markov chain Monte Carlo; Metropolis Hastings algorithm; Renewal theory; Reversible Markov chain; Spectral gap

Indexed keywords


EID: 14544277112     PISSN: 10505164     EISSN: None     Source Type: Journal    
DOI: 10.1214/105051604000000710     Document Type: Article
Times cited : (145)

References (23)
  • 1
    • 0042192904 scopus 로고
    • Uniform estimates for geometric ergodicity of recurrent Markov chains
    • Univ. Southern California
    • BAXENDALE, P. (1994). Uniform estimates for geometric ergodicity of recurrent Markov chains. Technical report, Univ. Southern California.
    • (1994) Technical Report
    • Baxendale, P.1
  • 2
    • 14544282666 scopus 로고    scopus 로고
    • Quantitative bounds on convergence of time-inhomogeneous Markov chains
    • DOUC, R., MOULINES, E. and ROSENTHAL, J. S. (2004). Quantitative bounds on convergence of time-inhomogeneous 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
  • 5
    • 0001967887 scopus 로고
    • Unitary dilations of Markov transition operators and the corresponding integral representation of transition probability matrices
    • (U. Grenander, ed.). Almqvist and Wiksell, Stockholm
    • KENDALL, D. G. (1959). Unitary dilations of Markov transition operators and the corresponding integral representation of transition probability matrices. In Probability and Statistics (U. Grenander, ed.) 138-161. Almqvist and Wiksell, Stockholm.
    • (1959) Probability and Statistics , pp. 138-161
    • Kendall, D.G.1
  • 6
    • 0000854270 scopus 로고
    • Covariance structure and convergence rate of the Gibbs sampler with various scans
    • LIU, J., WONG, W. and KONG, A. (1995). Covariance structure and convergence rate of the Gibbs sampler with various scans. J. R. Stat. Soc. Ser. B Stat. Methodol. 57 157-169.
    • (1995) J. R. Stat. Soc. Ser. B Stat. Methodol. , vol.57 , pp. 157-169
    • Liu, J.1    Wong, W.2    Kong, A.3
  • 7
    • 0030086282 scopus 로고    scopus 로고
    • Geometric convergence rates for stochastically ordered Markov chains
    • LUND, R. B. and TWEEDIE, R. L. (1996). Geometric convergence rates for stochastically ordered Markov chains. Math. Oper. Res. 21 182-194.
    • (1996) Math. Oper. Res. , vol.21 , pp. 182-194
    • Lund, R.B.1    Tweedie, R.L.2
  • 9
    • 0000566364 scopus 로고
    • Computable bounds for geometric convergence rates of Markov chains
    • MEYN, S. and TWEEDIE, R. (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.1    Tweedie, R.2
  • 11
    • 0000099991 scopus 로고
    • Geometric ergodicity of Harris recurrent Markov chains with applications to renewal theory
    • NUMMELIN, E. and TUOMINEN, P. (1982). Geometric ergodicity of Harris recurrent Markov chains with applications to renewal theory. Stochastic Process. Appl. 12 187-202.
    • (1982) Stochastic Process. Appl. , vol.12 , pp. 187-202
    • Nummelin, E.1    Tuominen, P.2
  • 12
    • 0010790837 scopus 로고
    • Geometric ergodicity and R-positivity for general Markov chains
    • NUMMELIN, E. and TWEEDIE, R. L. (1978). Geometric ergodicity and R-positivity for general Markov chains. Ann. Probab. 6 404-420.
    • (1978) Ann. Probab. , vol.6 , pp. 404-420
    • Nummelin, E.1    Tweedie, R.L.2
  • 13
    • 0002074149 scopus 로고    scopus 로고
    • Geometric ergodicity and hybrid Markov chains
    • ROBERTS, G. O. and ROSENTHAL, J. S. (1997). Geometric ergodicity and hybrid Markov chains. Electron. Comm. Probab. 2 13-25.
    • (1997) Electron. Comm. Probab. , vol.2 , pp. 13-25
    • Roberts, G.O.1    Rosenthal, J.S.2
  • 14
    • 0013091695 scopus 로고    scopus 로고
    • Shift-coupling and convergence rates of ergodic averages
    • ROBERTS, G. O. and ROSENTHAL, J. S. (1999). Shift-coupling and convergence rates of ergodic averages. Comm. Statist. Stochastic Models 13 147-165.
    • (1999) Comm. Statist. Stochastic Models , vol.13 , pp. 147-165
    • Roberts, G.O.1    Rosenthal, J.S.2
  • 15
    • 0001514831 scopus 로고    scopus 로고
    • Bounds on regeneration times and convergence rates for Markov chains
    • ROBERTS, G. O. and TWEEDIE, R. L. (1999). Bounds on regeneration times and convergence rates for Markov chains. Stochastic. Process. Appl. 80 211-229.
    • (1999) Stochastic. Process. Appl. , vol.80 , pp. 211-229
    • Roberts, G.O.1    Tweedie, R.L.2
  • 16
    • 0034196166 scopus 로고    scopus 로고
    • Rates of convergence of stochastically monotone and continuous time Markov models
    • ROBERTS, G. O. and TWEEDIE, R. L. (2000). Rates of convergence of stochastically monotone and continuous time Markov models. J. Appl. Probab. 37 359-373.
    • (2000) J. Appl. Probab. , vol.37 , pp. 359-373
    • Roberts, G.O.1    Tweedie, R.L.2
  • 17
    • 0013046167 scopus 로고    scopus 로고
    • 1 convergence are equivalent for reversible Markov chains. Probability, statistics and seismology
    • 1 convergence are equivalent for reversible Markov chains. Probability, statistics and seismology. J. Appl. Probab. 38A 37-41.
    • (2001) J. Appl. Probab. , vol.38 A , pp. 37-41
    • Roberts, G.O.1    Tweedie, R.L.2
  • 18
    • 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
  • 19
    • 3042638629 scopus 로고    scopus 로고
    • Quantitative convergence rates of Markov chains: A simple account
    • ROSENTHAL, J. S. (2002). Quantitative convergence rates of Markov chains: A simple account. Electron. Comm. Probab. 7 123-128.
    • (2002) Electron. Comm. Probab. , vol.7 , pp. 123-128
    • Rosenthal, J.S.1
  • 20
    • 0037364893 scopus 로고    scopus 로고
    • Asymptotic variance and convergence rates of nearly periodic MCMC algorithms
    • ROSENTHAL, J. S. (2003). Asymptotic variance and convergence rates of nearly periodic MCMC algorithms. J. Amer. Statist. Assoc. 98 169-177.
    • (2003) J. Amer. Statist. Assoc. , vol.98 , pp. 169-177
    • Rosenthal, J.S.1
  • 22
    • 14544299017 scopus 로고
    • On the spectra of some linear operators associated with queuing systems
    • VERE-JONES, D. (1963). On the spectra of some linear operators associated with queuing systems. Z. Wahrsch. Verw. Gebiete 2 12-21.
    • (1963) Z. Wahrsch. Verw. Gebiete , vol.2 , pp. 12-21
    • Vere-Jones, D.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.