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Volumn 38, Issue 5, 2010, Pages 2823-2856

Trajectory averaging for stochastic approximation MCMC algorithms

Author keywords

Asymptotic efficiency; Convergence; Markov chain Monte Carlo; Stochastic approximation Monte Carlo; Trajectory averaging

Indexed keywords


EID: 77957597582     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/10-AOS807     Document Type: Article
Times cited : (21)

References (43)
  • 1
    • 33750512542 scopus 로고    scopus 로고
    • On the ergodicity properties of some adaptive MCMC algorithms
    • DOI 10.1214/105051606000000286
    • ANDRIEU, C. and MOULINES, É. (2006). On the ergodicity properties of some adaptive MCMC algorithms. Ann. Appl. Probab. 16 1462-1505. MR2260070 (Pubitemid 44662199)
    • (2006) Annals of Applied Probability , vol.16 , Issue.3 , pp. 1462-1505
    • Andrieu, C.1    Moulines, E.2
  • 2
    • 33244461073 scopus 로고    scopus 로고
    • Stability of stochastic approximation under verifiable conditions
    • MR2177157
    • ANDRIEU, C., MOULINES, É. and PRIOURET, P. (2005). Stability of stochastic approximation under verifiable conditions. SIAM J. Control Optim. 44 283-312. MR2177157
    • (2005) SIAM J. Control Optim. , vol.44 , pp. 283-312
    • Andrieu, C.1    Moulines, É.2    Priouret, P.3
  • 3
    • 77949412635 scopus 로고    scopus 로고
    • TheWang-Landau algorithm in general state spaces: Applications and convergence analysis
    • ATCHADÉ, Y. F. and LIU, J. S. (2010). TheWang-Landau algorithm in general state spaces: Applications and convergence analysis. Statist. Sinica 20 209-233.
    • (2010) Statist. Sinica , vol.20 , pp. 209-233
    • Atchadé, Y.F.1    Liu, J.S.2
  • 5
    • 33845617570 scopus 로고    scopus 로고
    • Cesàro a-integrability and laws of large numbers. II
    • MR2279604
    • CHANDRA, T. K. and GOSWAMI, A. (2006). Ces?ro a-integrability and laws of large numbers. II. J. Theoret. Probab. 19 789-816. MR2279604
    • (2006) J. Theoret. Probab. , vol.19 , pp. 789-816
    • Chandra, T.K.1    Goswami, A.2
  • 6
    • 0002700406 scopus 로고
    • Asymptotically efficient stochastic approximation
    • MR1277359
    • CHEN, H. F. (1993). Asymptotically efficient stochastic approximation. Stochastics Stochastics Rep. 45 1-16. MR1277359
    • (1993) Stochastics Stochastics Rep. , vol.45 , pp. 1-16
    • Chen, H.F.1
  • 8
    • 38249037320 scopus 로고
    • Convergence and robustness of the Robbins-Monro algorithm truncated at randomly varying bounds
    • MR0931029
    • CHEN, H. F., GUO, L. and GAO, A. (1988). Convergence and robustness of the Robbins-Monro algorithm truncated at randomly varying bounds. Stochastic Process. Appl. 27 217-231. MR0931029
    • (1988) Stochastic Process. Appl. , vol.27 , pp. 217-231
    • Chen, H.F.1    Guo, L.2    Gao, A.3
  • 9
    • 0011595015 scopus 로고
    • Stochastic approximation procedures with randomly varying truncations
    • MR0869196
    • CHEN, H. F. and ZHU, Y. M. (1986). Stochastic approximation procedures with randomly varying truncations. Sci. Sinica Ser. A 29 914-926. MR0869196
    • (1986) Sci. Sinica Ser. A , vol.29 , pp. 914-926
    • Chen, H.F.1    Zhu, Y.M.2
  • 10
    • 37349095257 scopus 로고    scopus 로고
    • Phylogenetic tree reconstruction using sequential stochastic approximation Monte Carlo
    • CHEON, S. and LIANG, F. (2007). Phylogenetic tree reconstruction using sequential stochastic approximation Monte Carlo. BioSystems 91 94-107.
    • (2007) BioSystems , vol.91 , pp. 94-107
    • Cheon, S.1    Liang, F.2
  • 11
    • 69049104015 scopus 로고    scopus 로고
    • Bayesian phylogeny analysis via stochastic approximationMonte Carlo
    • CHEON, S. and LIANG, F. (2009). Bayesian phylogeny analysis via stochastic approximationMonte Carlo. Mol. Phylog. Evol. 53 394-403.
    • (2009) Mol. Phylog. Evol. , vol.53 , pp. 394-403
    • Cheon, S.1    Liang, F.2
  • 12
    • 0033243858 scopus 로고    scopus 로고
    • Convergence of a stochastic approximation version of the em algorithm
    • MR1701103
    • DELYON, B., LAVIELLE, M. andMOULINES, E. (1999). Convergence of a stochastic approximation version of the EM algorithm. Ann. Statist. 27 94-128. MR1701103
    • (1999) Ann. Statist. , vol.27 , pp. 94-128
    • Delyon, B.1    Lavielle, M.2    Moulines, E.3
  • 13
    • 0031233853 scopus 로고    scopus 로고
    • Weighted means in stochastic approximation of minima
    • MR1466929
    • DIPPON, J. and RENZ, J. (1997). Weighted means in stochastic approximation of minima. SIAM J. Control Optim. 35 1811-1827. MR1466929
    • (1997) SIAM J. Control Optim. , vol.35 , pp. 1811-1827
    • Dippon, J.1    Renz, J.2
  • 16
    • 84950437936 scopus 로고
    • Annealing Markov chain Monte Carlo with applications to ancestral inference
    • GEYER, C. J. and THOMPSON, E. A. (1995). Annealing Markov chain Monte Carlo with applications to ancestral inference. J. Amer. Statist. Assoc. 90 909-920.
    • (1995) J. Amer. Statist. Assoc. , vol.90 , pp. 909-920
    • Geyer, C.J.1    Thompson, E.A.2
  • 17
    • 13144294075 scopus 로고    scopus 로고
    • A stochastic approximation algorithm with Markov chain Monte Carlo method for incomplete data estimation problems
    • MR1630899
    • GU, M. G. and KONG, F. H. (1998). A stochastic approximation algorithm with Markov chain Monte Carlo method for incomplete data estimation problems. Proc. Natl. Acad. Sci. USA 95 7270-7274. MR1630899
    • (1998) Proc. Natl. Acad. Sci. USA , vol.95 , pp. 7270-7274
    • Gu, M.G.1    Kong, F.H.2
  • 18
    • 0035532138 scopus 로고    scopus 로고
    • Maximum likelihood estimation for spatial models by Markov chain Monte Carlo stochastic approximation
    • MR1841419
    • GU, M. G. and ZHU, H. T. (2001). Maximum likelihood estimation for spatial models by Markov chain Monte Carlo stochastic approximation. J. R. Stat. Soc. Ser. B Stat. Methodol. 63 339-355. MR1841419
    • (2001) J. R. Stat. Soc. Ser. B Stat. Methodol. , vol.63 , pp. 339-355
    • Gu, M.G.1    Zhu, H.T.2
  • 19
    • 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
  • 20
    • 0027627789 scopus 로고
    • Stochastic approximation with averaging of the iterates: Optimal asymptotic rate of convergence for general processes
    • MR1227546
    • KUSHNER, H. J. and YANG, J. (1993). Stochastic approximation with averaging of the iterates: Optimal asymptotic rate of convergence for general processes. SIAM J. Control Optim. 31 1045-1062. MR1227546
    • (1993) SIAM J. Control Optim. , vol.31 , pp. 1045-1062
    • Kushner, H.J.1    Yang, J.2
  • 21
    • 0029221295 scopus 로고
    • Stochastic approximation with averaging and feedback: Rapidly convergent "on-line" algorithms
    • MR1344315
    • KUSHNER, H. J. and YANG, J. (1995). Stochastic approximation with averaging and feedback: Rapidly convergent "on-line" algorithms. IEEE Trans. Automat. Control 40 24-34. MR1344315
    • (1995) IEEE Trans. Automat. Control , vol.40 , pp. 24-34
    • Kushner, H.J.1    Yang, J.2
  • 23
    • 29144446035 scopus 로고    scopus 로고
    • Generalized Wang-Landau algorithm for Monte Carlo computation
    • MR2236444
    • LIANG, F. (2005). Generalized Wang-Landau algorithm for Monte Carlo computation. J. Amer. Statist. Assoc. 100 1311-1327. MR2236444
    • (2005) J. Amer. Statist. Assoc. , vol.100 , pp. 1311-1327
    • Liang, F.1
  • 24
    • 35348968551 scopus 로고    scopus 로고
    • Continuous contour Monte Carlo for marginal density estimation with an application to a spatial statistical model
    • MR2351082
    • LIANG, F. (2007a). Continuous contour Monte Carlo for marginal density estimation with an application to a spatial statistical model. J. Comp. Graph. Statist. 16 608-632. MR2351082
    • (2007) J. Comp. Graph. Statist. , vol.16 , pp. 608-632
    • Liang, F.1
  • 25
    • 34548179892 scopus 로고    scopus 로고
    • Annealing stochastic approximation Monte Carlo for neural network training
    • LIANG, F. (2007b). Annealing stochastic approximation Monte Carlo for neural network training. Mach. Learn. 68 201-233.
    • (2007) Mach. Learn. , vol.68 , pp. 201-233
    • Liang, F.1
  • 26
    • 69049089832 scopus 로고    scopus 로고
    • Improving SAMC using smoothing methods: Theory and applications to Bayesian model selection problems
    • MR2541441
    • LIANG, F. (2009). Improving SAMC using smoothing methods: Theory and applications to Bayesian model selection problems. Ann. Statist. 37 2626-2654. MR2541441
    • (2009) Ann. Statist. , vol.37 , pp. 2626-2654
    • Liang, F.1
  • 27
    • 33947215681 scopus 로고    scopus 로고
    • Stochastic approximation in Monte Carlo computation
    • MR2345544
    • LIANG, F., LIU, C. and CARROLL, R. J. (2007). Stochastic approximation in Monte Carlo computation. J. Amer. Statist. Assoc. 102 305-320. MR2345544
    • (2007) J. Amer. Statist. Assoc. , vol.102 , pp. 305-320
    • Liang, F.1    Liu, C.2    Carroll, R.J.3
  • 28
    • 58549098419 scopus 로고    scopus 로고
    • Learning Bayesian networks for discrete data
    • LIANG, F. and ZHANG, J. (2009). Learning Bayesian networks for discrete data. Comput. Statist. Data Anal. 53 865-876.
    • (2009) Comput. Statist. Data Anal. , vol.53 , pp. 865-876
    • Liang, F.1    Zhang, J.2
  • 29
    • 33644899039 scopus 로고
    • Simulated tempering: A new Monte Carlo scheme
    • MARINARI, E. and 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
  • 31
    • 0002755026 scopus 로고
    • Stochastic approximation of the MLE for a spatial point pattern
    • MR1115181
    • MOYEED, R. A. and BADDELEY, A. J. (1991). Stochastic approximation of the MLE for a spatial point pattern. Scand. J. Statist. 18 39-50. MR1115181
    • (1991) Scand. J. Statist. , vol.18 , pp. 39-50
    • Moyeed, R.A.1    Baddeley, A.J.2
  • 32
    • 0034462128 scopus 로고    scopus 로고
    • Asymptotic almost sure efficiency of averaged stochastic algorithms
    • MR1780908
    • PELLETIER, M. (2000). Asymptotic almost sure efficiency of averaged stochastic algorithms. SIAM J. Control Optim. 39 49-72. MR1780908
    • (2000) SIAM J. Control Optim. , vol.39 , pp. 49-72
    • Pelletier, M.1
  • 33
    • 0000828406 scopus 로고
    • New stochastic approximation type procedures
    • (in Russian). MR1071220
    • POLYAK, B. T. (1990). New stochastic approximation type procedures. Avtomat. i Telemekh. 7 98-107 (in Russian). MR1071220
    • (1990) Avtomat. i Telemekh. , vol.7 , pp. 98-107
    • Polyak, B.T.1
  • 34
    • 0026899240 scopus 로고
    • Acceleration of stochastic approximation by averaging
    • MR1167814
    • POLYAK, B. T. and JUDITSKY, A. B. (1992). Acceleration of stochastic approximation by averaging. SIAM J. Control Optim. 30 838-855. MR1167814
    • (1992) SIAM J. Control Optim. , vol.30 , pp. 838-855
    • Polyak, B.T.1    Juditsky, A.B.2
  • 35
    • 0000016172 scopus 로고
    • A stochastic approximation method
    • MR0042668
    • ROBBINS, H. and MONRO, S. (1951). A stochastic approximation method. Ann. Math. Statist. 22 400-407. MR0042668
    • (1951) Ann. Math. Statist. , vol.22 , pp. 400-407
    • Robbins, H.1    Monro, S.2
  • 37
    • 0031384060 scopus 로고    scopus 로고
    • Convergence of stochastic approximation under general noise and stability conditions
    • IEEE Systems Society, San Diego, CA
    • TADÍC , V. (1997). Convergence of stochastic approximation under general noise and stability conditions. In: Proceedings of the 36th IEEE Conference on Decision and Control 3 2281-2286. IEEE Systems Society, San Diego, CA.
    • (1997) Proceedings of the 36thIEEE Conference on Decision and Control , vol.3 , pp. 2281-2286
    • Tadíc, V.1
  • 38
    • 0033184357 scopus 로고    scopus 로고
    • Asymptotic efficiency of perturbationanalysis-based stochastic approximation with averaging
    • MR1720140
    • TANG, Q. Y., L'ECUYER, P. and CHEN, H. F. (1999). Asymptotic efficiency of perturbationanalysis-based stochastic approximation with averaging. SIAM J. Control Optim. 37 1822-1847. MR1720140
    • (1999) SIAM J. Control Optim. , vol.37 , pp. 1822-1847
    • Tang, Q.Y.1    L'Ecuyer, P.2    Chen, H.F.3
  • 39
    • 6644221271 scopus 로고    scopus 로고
    • Efficient, multiple-range random walk algorithm to calculate the density of states
    • WANG, F. and LANDAU, D. P. (2001). Efficient, multiple-range random walk algorithm to calculate the density of states. Phys. Rev. Lett. 86 2050-2053.
    • (2001) Phys. Rev. Lett. , vol.86 , pp. 2050-2053
    • Wang, F.1    Landau, D.P.2
  • 41
    • 0000355193 scopus 로고
    • Parametric inference for imperfectly observed Gibbsian fields
    • MR1002904
    • YOUNES, L. (1989). Parametric inference for imperfectly observed Gibbsian fields. Probab. Theory Related Fields 82 625-645. MR1002904
    • (1989) Probab. Theory Related Fields , vol.82 , pp. 625-645
    • Younes, L.1
  • 42
    • 33644756784 scopus 로고    scopus 로고
    • On the convergence ofMarkovian stochastic algorithms with rapidly decreasing ergodicity rates
    • MR1687636
    • YOUNES, L. (1999). On the convergence ofMarkovian stochastic algorithms with rapidly decreasing ergodicity rates. Stochastics Stochastics Rep. 65 177-228. MR1687636
    • (1999) Stochastics Stochastics Rep. , vol.65 , pp. 177-228
    • Younes, L.1


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