메뉴 건너뛰기




Volumn 63, Issue 2, 2001, Pages 339-355

Maximum likelihood estimation for spatial models by Markov chain Monte Carlo stochastic approximation

Author keywords

Auto normal model; Ising model; Markov chain Monte Carlo methods; Off line average; Spatial models; Stochastic approximation; Very soft core model

Indexed keywords


EID: 0035532138     PISSN: 13697412     EISSN: None     Source Type: Journal    
DOI: 10.1111/1467-9868.00289     Document Type: Article
Times cited : (85)

References (53)
  • 2
    • 0005459531 scopus 로고    scopus 로고
    • Practical maximum pseudo-likelihood for spatial point patterns
    • Baddeley, A. J. and Turner, R. (2000) Practical maximum pseudo-likelihood for spatial point patterns (with discussion). Aust. New Z. J. Statist., 42, 283-322.
    • (2000) Aust. New Z. J. Statist. , vol.42 , pp. 283-322
    • Baddeley, A.J.1    Turner, R.2
  • 4
    • 0000913755 scopus 로고
    • Spatial interaction and the statistical analysis of lattice systems
    • Besag, J. E. (1974) Spatial interaction and the statistical analysis of lattice systems (with discussion). J. R. Statist. Soc. B, 36, 192-236.
    • (1974) J. R. Statist. Soc. B , vol.36 , pp. 192-236
    • Besag, J.E.1
  • 5
    • 0017751656 scopus 로고
    • Efficiency of pseudo likelihood estimators for simple Gaussian fields
    • -(1977) Efficiency of pseudo likelihood estimators for simple Gaussian fields. Biometrika, 64, 616-618.
    • (1977) Biometrika , vol.64 , pp. 616-618
  • 6
    • 0000103562 scopus 로고
    • Spatial statistics and Bayesian computation
    • Besag, J. and Green, P. J. (1993) Spatial statistics and Bayesian computation. J. R. Statist. Soc. B, 55, 25-37.
    • (1993) J. R. Statist. Soc. B , vol.55 , pp. 25-37
    • Besag, J.1    Green, P.J.2
  • 7
    • 0141477361 scopus 로고
    • Bayesian computation and stochastic systems
    • Besag, J. E., Green, P., Higdon, D. and Mengersen, K. (1995) Bayesian computation and stochastic systems (with discussion). Statist. Sci., 10, 3-66.
    • (1995) Statist. Sci. , vol.10 , pp. 3-66
    • Besag, J.E.1    Green, P.2    Higdon, D.3    Mengersen, K.4
  • 8
    • 0016697211 scopus 로고
    • On the estimation and testing of spatial interaction in Gaussian lattice processes
    • Besag, J. E. and Moran, P. A. P. (1975) On the estimation and testing of spatial interaction in Gaussian lattice processes. Biometrika, 62, 555-562.
    • (1975) Biometrika , vol.62 , pp. 555-562
    • Besag, J.E.1    Moran, P.A.P.2
  • 9
    • 0033475053 scopus 로고    scopus 로고
    • Maximizing generalized linear mixed model likelihoods with an automated Monte Carlo EM algorithm
    • Booth, J. G. and Hobert, J. P. (1999) Maximizing generalized linear mixed model likelihoods with an automated Monte Carlo EM algorithm. J. R. Statist. Soc. B, 61, 265-285.
    • (1999) J. R. Statist. Soc. B , vol.61 , pp. 265-285
    • Booth, J.G.1    Hobert, J.P.2
  • 11
    • 38249037320 scopus 로고
    • Convergence and robustness of the Robbins-Monro algorithm truncated at randomly varying bounds
    • Chen, H. F., Guo, L. and Gao, A. J. (1988) Convergence and robustness of the Robbins-Monro algorithm truncated at randomly varying bounds. Stoch. Processes Applic., 27, 217-231.
    • (1988) Stoch. Processes Applic. , vol.27 , pp. 217-231
    • Chen, H.F.1    Guo, L.2    Gao, A.J.3
  • 12
    • 0000695777 scopus 로고
    • On consistency of a class of estimators for exponential families of Markov random fields on the lattice
    • Comets, F. (1992) On consistency of a class of estimators for exponential families of Markov random fields on the lattice. Ann. Statist., 20, 455-468.
    • (1992) Ann. Statist. , vol.20 , pp. 455-468
    • Comets, F.1
  • 14
    • 0033243858 scopus 로고    scopus 로고
    • Convergence of a stochastic approximation version of the EM algorithm
    • Delyon, B., Lavielle, E. and Moulines, E. (1999) Convergence of a stochastic approximation version of the EM algorithm. Ann. Statist., 27, 94-128.
    • (1999) Ann. Statist. , vol.27 , pp. 94-128
    • Delyon, B.1    Lavielle, E.2    Moulines, E.3
  • 18
    • 84972492387 scopus 로고
    • Inference from iterative simulation using multiple sequences
    • Gelman, A. and Rubin, D. B. (1992) Inference from iterative simulation using multiple sequences (with discussion). Statist. Sci., 7, 457-511.
    • (1992) Statist. Sci. , vol.7 , pp. 457-511
    • Gelman, A.1    Rubin, D.B.2
  • 19
    • 0002218961 scopus 로고    scopus 로고
    • Likelihood inference for spatial point processes
    • (eds O. E. Barndorff-Nielsen, W. S. Kendall and M. C. van Lieshout). London: Chapman and Hall
    • Geyer, C. J. (1999) Likelihood inference for spatial point processes. In Stochastic Geometry: Likelihood and Computation (eds O. E. Barndorff-Nielsen, W. S. Kendall and M. C. van Lieshout). London: Chapman and Hall.
    • (1999) Stochastic Geometry: Likelihood and Computation
    • Geyer, C.J.1
  • 20
    • 0000051109 scopus 로고
    • Constrained Monte Carlo maximum likelihood for dependent data
    • Geyer, C. J. and Thompson, E. A. (1992) Constrained Monte Carlo maximum likelihood for dependent data (with discussion). J. R. Statist. Soc. B, 54, 657-699.
    • (1992) J. R. Statist. Soc. B , vol.54 , pp. 657-699
    • Geyer, C.J.1    Thompson, E.A.2
  • 21
    • 0040304544 scopus 로고    scopus 로고
    • Parameter estimation for marked Gibbs point processes through the maximum pseudo likelihood method
    • Goulard, M., Särkkä, A. and Grabarnik, P. (1996) Parameter estimation for marked Gibbs point processes through the maximum pseudo likelihood method. Scand. J. Statist., 23, 365-379.
    • (1996) Scand. J. Statist. , vol.23 , pp. 365-379
    • Goulard, M.1    Särkkä, A.2    Grabarnik, P.3
  • 22
    • 13144294075 scopus 로고    scopus 로고
    • A stochastic approximation algorithm with Markov chain Monte Carlo method for incomplete data estimation problems
    • Gu, M. G. and Kong, F. H. (1998) A stochastic approximation algorithm with Markov chain Monte Carlo method for incomplete data estimation problems. Proc. Natn. Acad. Sci. USA, 95, 7270-7274.
    • (1998) Proc. Natn. Acad. Sci. USA , vol.95 , pp. 7270-7274
    • Gu, M.G.1    Kong, F.H.2
  • 23
    • 0002803975 scopus 로고
    • Parameter estimation for a stationary process on a d-dimensional lattice
    • Guyon, X. (1982) Parameter estimation for a stationary process on a d-dimensional lattice. Biometrika, 69, 95-105.
    • (1982) Biometrika , vol.69 , pp. 95-105
    • Guyon, X.1
  • 24
    • 0345044901 scopus 로고    scopus 로고
    • Multitype spatial point patterns with hierarchical interactions
    • Högmander, H. and Särkkä, A. (1999) Multitype spatial point patterns with hierarchical interactions. Biometrics, 55, 1051-1058.
    • (1999) Biometrics , vol.55 , pp. 1051-1058
    • Högmander, H.1    Särkkä, A.2
  • 25
    • 0033245942 scopus 로고    scopus 로고
    • Improvements of the maximum pseudo-likelihood estimators in various spatial statistical models
    • Huang, F. and Ogata, Y. (1999) Improvements of the maximum pseudo-likelihood estimators in various spatial statistical models. J. Comput. Graph. Statist., 8, 510-530.
    • (1999) J. Comput. Graph. Statist. , vol.8 , pp. 510-530
    • Huang, F.1    Ogata, Y.2
  • 26
    • 0031799834 scopus 로고    scopus 로고
    • Markov chain Monte Carlo for auto-logistic regression models with application to the distribution of plant species
    • Huffer, F. W. and Wu, H. L. (1998) Markov chain Monte Carlo for auto-logistic regression models with application to the distribution of plant species. Biometrics, 54, 509-524.
    • (1998) Biometrics , vol.54 , pp. 509-524
    • Huffer, F.W.1    Wu, H.L.2
  • 27
    • 0003230531 scopus 로고
    • DALL: Davidon's algorithm for log likelihood maximization - a FORTRAN subroutine for statistical model builders
    • Ishiguro, M. and Akaike, H. (1989) DALL: Davidon's algorithm for log likelihood maximization - a FORTRAN subroutine for statistical model builders. Comput. Sci. Monogr., 25.
    • (1989) Comput. Sci. Monogr. , vol.25
    • Ishiguro, M.1    Akaike, H.2
  • 28
    • 0000849716 scopus 로고
    • Pseudolikelihood for exponential family models of spatial point processes
    • Jensen, J. L. and Møller, J. (1991) Pseudolikelihood for exponential family models of spatial point processes. Ann. Appl. Probab., 1, 445-461.
    • (1991) Ann. Appl. Probab. , vol.1 , pp. 445-461
    • Jensen, J.L.1    Møller, J.2
  • 29
    • 0017154989 scopus 로고
    • A note on Strauss's model for clustering
    • Kelly, F. P. and Ripley, B. D. (1976) A note on Strauss's model for clustering. Biometrika, 63, 357-360.
    • (1976) Biometrika , vol.63 , pp. 357-360
    • Kelly, F.P.1    Ripley, B.D.2
  • 30
    • 0002803115 scopus 로고
    • Accelerated stochastic approximation
    • Kesten, H. (1957) Accelerated stochastic approximation. Ann. Math. Statist., 28, 41-59.
    • (1957) Ann. Math. Statist. , vol.28 , pp. 41-59
    • Kesten, H.1
  • 32
    • 21844496539 scopus 로고
    • Consistency of the maximum pseudo-likelihood estimator of continuous state space Gibbsian processes
    • Mase, S. (1995) Consistency of the maximum pseudo-likelihood estimator of continuous state space Gibbsian processes. Ann. Appl. Probab., 5, 603-612.
    • (1995) Ann. Appl. Probab. , vol.5 , pp. 603-612
    • Mase, S.1
  • 33
    • 0001625977 scopus 로고    scopus 로고
    • Markov chain Monte Carlo and spatial point processes
    • (eds O. E. Barndorff-Nielsen, W. S. Kendall and M. C. van Lieshout). London: Chapman and Hall
    • Møller, J. (1999) Markov chain Monte Carlo and spatial point processes. In Stochastic Geometry: Likelihood and Computation (eds O. E. Barndorff-Nielsen, W. S. Kendall and M. C. van Lieshout). London: Chapman and Hall.
    • (1999) Stochastic Geometry: Likelihood and Computation
    • Møller, J.1
  • 34
    • 0002337198 scopus 로고
    • A Gaussian Markovian process on a square lattice
    • Moran, P. A. P. (1973) A Gaussian Markovian process on a square lattice. J. Appl. Probab., 10, 54-62.
    • (1973) J. Appl. Probab. , vol.10 , pp. 54-62
    • Moran, P.A.P.1
  • 35
    • 0002755026 scopus 로고
    • Stochastic approximation of the MLE for a spatial point pattern
    • Moyeed, R. A. and Baddeley, A. J. (1991) Stochastic approximation of the MLE for a spatial point pattern. Scand. J. Statist., 18, 39-50.
    • (1991) Scand. J. Statist. , vol.18 , pp. 39-50
    • Moyeed, R.A.1    Baddeley, A.J.2
  • 36
    • 0003606575 scopus 로고
    • A generic approach to posterior integration and Gibbs sampling
    • Purdue University, West Lafayette
    • Müller, P. (1991) A generic approach to posterior integration and Gibbs sampling. Technical Report. Purdue University, West Lafayette.
    • (1991) Technical Report
    • Müller, P.1
  • 37
    • 0000333882 scopus 로고
    • Likelihood analysis of spatial point patterns
    • Ogata, Y. and Tanemura, M. (1984) Likelihood analysis of spatial point patterns. J. R. Statist. Soc. B, 46, 496-518.
    • (1984) J. R. Statist. Soc. B , vol.46 , pp. 496-518
    • Ogata, Y.1    Tanemura, M.2
  • 38
    • 0002230946 scopus 로고
    • Modelling interaction in spatial point patterns: Parameter estimation by the maximum likelihood method
    • Penttinen, A. (1984) Modelling interaction in spatial point patterns: parameter estimation by the maximum likelihood method. Jy. Stud. Comput. Sci. Econometr. Statist., 7.
    • (1984) Jy. Stud. Comput. Sci. Econometr. Statist. , vol.7
    • Penttinen, A.1
  • 39
    • 0007243850 scopus 로고
    • Inference for general Ising models
    • Pickard, D. K. (1982) Inference for general Ising models. J. Appl. Probab. A, 19, 345-357.
    • (1982) J. Appl. Probab. A , vol.19 , pp. 345-357
    • Pickard, D.K.1
  • 40
    • 0000828406 scopus 로고
    • New stochastic approximation type procedures
    • Polyak, B. T. (1990) New stochastic approximation type procedures. Autom. Telem., 98-107. (Engl. transl. Autom. Remote Contr., 51, 937-946.)
    • (1990) Autom. Telem. , pp. 98-107
    • Polyak, B.T.1
  • 41
    • 0007250793 scopus 로고    scopus 로고
    • Polyak, B. T. (1990) New stochastic approximation type procedures. Autom. Telem., 98-107. (Engl. transl. Autom. Remote Contr., 51, 937-946.)
    • Engl. Transl. Autom. Remote Contr. , vol.51 , pp. 937-946
  • 42
    • 0026899240 scopus 로고
    • Acceleration of stochastic approximation by averaging
    • Polyak, B. T. and Juditski, A. B. (1992) Acceleration of stochastic approximation by averaging. SIAM J. Contr. Optimzn, 30, 838-855.
    • (1992) SIAM J. Contr. Optimzn , vol.30 , pp. 838-855
    • Polyak, B.T.1    Juditski, A.B.2
  • 43
    • 0000135848 scopus 로고
    • Modelling spatial patterns
    • Ripley, B. D. (1977) Modelling spatial patterns (with discussion). J. R. Statist. Soc. B, 39, 172-212.
    • (1977) J. R. Statist. Soc. B , vol.39 , pp. 172-212
    • Ripley, B.D.1
  • 44
    • 0003604116 scopus 로고
    • New York: Wiley
    • -(1981) Spatial Statistics. New York: Wiley.
    • (1981) Spatial Statistics
  • 45
    • 0000016172 scopus 로고
    • A stochastic approximation method
    • Robbins, H. and Monro, S. (1951) A stochastic approximation method. Ann. Math. Statist., 22, 400-407.
    • (1951) Ann. Math. Statist. , vol.22 , pp. 400-407
    • Robbins, H.1    Monro, S.2
  • 47
    • 0035649131 scopus 로고    scopus 로고
    • Fast sampling of Gaussian Markov random fields
    • Rue, H. (2001) Fast sampling of Gaussian Markov random fields. J. R. Statist. Soc. B, 63, 325-338.
    • (2001) J. R. Statist. Soc. B , vol.63 , pp. 325-338
    • Rue, H.1
  • 50
    • 0016689445 scopus 로고
    • A model for clustering
    • Strauss, D. J. (1975) A model for clustering. Biometrika, 62, 467-475.
    • (1975) Biometrika , vol.62 , pp. 467-475
    • Strauss, D.J.1
  • 51
    • 0017471706 scopus 로고
    • Clustering on coloured lattices
    • -(1977) Clustering on coloured lattices. J. Appl. Probab., 14, 135-143.
    • (1977) J. Appl. Probab. , vol.14 , pp. 135-143
  • 52
    • 0000490897 scopus 로고
    • Estimation and annealing of Gibbsian fields
    • Younes, L. (1988) Estimation and annealing of Gibbsian fields. Ann. Inst. H. Poincaré, 24, 269-294.
    • (1988) Ann. Inst. H. Poincaré , vol.24 , pp. 269-294
    • Younes, L.1
  • 53
    • 0000355193 scopus 로고
    • Parameter estimation for imperfectly observed Gibbsian fields
    • -(1989) Parameter estimation for imperfectly observed Gibbsian fields. Probab. Theory Reltd Flds, 82, 625-645.
    • (1989) Probab. Theory Reltd Flds , vol.82 , pp. 625-645


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.