메뉴 건너뛰기




Volumn 66, Issue 4, 2004, Pages 877-892

Approximating hidden Gaussian Markov random fields

Author keywords

Block sampling; Conditional autoregressive model; Gaussian Markov random field; Hidden Markov models; Markov chain Monte Carlo methods; Metropolized independence sampler; Sequential Monte Carlo methods

Indexed keywords


EID: 8644271571     PISSN: 13697412     EISSN: None     Source Type: Journal    
DOI: 10.1111/j.1467-9868.2004.B5590.x     Document Type: Article
Times cited : (28)

References (50)
  • 1
    • 0001143218 scopus 로고
    • A candidate's formula: A curious result in Bayesian prediction
    • Besag, J. (1989) A candidate's formula: a curious result in Bayesian prediction. Biometrika, 76, 183.
    • (1989) Biometrika , vol.76 , pp. 183
    • Besag, J.1
  • 2
    • 0040836224 scopus 로고
    • Discussion on 'Representations of knowledge in complex systems' (by U. Grenander and M. I. Miller)
    • Besag, J. (1994) Discussion on 'Representations of knowledge in complex systems' (by U. Grenander and M. I. Miller). J. R. Statist. Soc. B, 56, 591-592.
    • (1994) J. R. Statist. Soc. B , vol.56 , pp. 591-592
    • Besag, J.1
  • 3
    • 0033482454 scopus 로고    scopus 로고
    • Bayesian analysis of agricultural field experiments
    • Besag, J. and Higdon, D. (1999) Bayesian analysis of agricultural field experiments (with discussion). J. R. Statist. Soc. B, 61, 691-746.
    • (1999) J. R. Statist. Soc. B , vol.61 , pp. 691-746
    • Besag, J.1    Higdon, D.2
  • 4
    • 33845221523 scopus 로고
    • On conditional and intrinsic autoregressions
    • Besag, J. and Kooperberg, C. (1995) On conditional and intrinsic autoregressions. Biometrika, 82, 733-746.
    • (1995) Biometrika , vol.82 , pp. 733-746
    • Besag, J.1    Kooperberg, C.2
  • 5
    • 28344449679 scopus 로고
    • Bayesian image restoration with two applications in spatial statistics
    • Besag, J., York, J. and Mollié, A. (1991) Bayesian image restoration with two applications in spatial statistics (with discussion). Ann. Inst. Statist. Math., 43, 1-59.
    • (1991) Ann. Inst. Statist. Math. , vol.43 , pp. 1-59
    • Besag, J.1    York, J.2    Mollié, A.3
  • 6
    • 8644285268 scopus 로고    scopus 로고
    • Empirical supremum rejection sampling
    • Caffo, B. S., Booth, J. G. and Davison, A. C. (2002) Empirical supremum rejection sampling. Biometrika, 89, 745-754.
    • (2002) Biometrika , vol.89 , pp. 745-754
    • Caffo, B.S.1    Booth, J.G.2    Davison, A.C.3
  • 7
    • 0000193853 scopus 로고
    • On Gibbs sampling for state space models
    • Carter, C. K. and Kohn, R. (1994) On Gibbs sampling for state space models. Biometrika, 81, 541-543.
    • (1994) Biometrika , vol.81 , pp. 541-543
    • Carter, C.K.1    Kohn, R.2
  • 8
    • 0012338718 scopus 로고    scopus 로고
    • A sequential particle filter method for static models
    • Chopin, N. (2002) A sequential particle filter method for static models. Biometrika, 89, 539-552.
    • (2002) Biometrika , vol.89 , pp. 539-552
    • Chopin, N.1
  • 10
    • 8644242518 scopus 로고    scopus 로고
    • Robust MCMC for spatial GLMM's
    • Preprints. Department of Mathematical Sciences, Lund University, Lund
    • Christensen, O. F., Roberts, G. O. and Sköld, M. (2003) Robust MCMC for spatial GLMM's. Preprints in Mathematical Sciences 23. Department of Mathematical Sciences, Lund University, Lund.
    • (2003) Mathematical Sciences 23
    • Christensen, O.F.1    Roberts, G.O.2    Sköld, M.3
  • 11
    • 0035989805 scopus 로고    scopus 로고
    • Bayesian prediction of spatial count data using generalized linear mixed models
    • Christensen, O. F. and Waagepetersen, R. P. (2002) Bayesian prediction of spatial count data using generalized linear mixed models. Biometrics, 58, 280-286.
    • (2002) Biometrics , vol.58 , pp. 280-286
    • Christensen, O.F.1    Waagepetersen, R.P.2
  • 14
    • 0040843494 scopus 로고    scopus 로고
    • Model-based geostatistics
    • Diggle, P. J., Tawn, J. A. and Moyeed, R. A. (1998) Model-based geostatistics (with discussion). Appl. Statist., 47, 299-350.
    • (1998) Appl. Statist. , vol.47 , pp. 299-350
    • Diggle, P.J.1    Tawn, J.A.2    Moyeed, R.A.3
  • 16
    • 0036017452 scopus 로고    scopus 로고
    • Adjusted maximum likelihood and pseudo-likelihood estimation for noisy Gaussian Markov random fields
    • Dryden, I. L., Ippoliti, L. and Romagnoli, L. (2002) Adjusted maximum likelihood and pseudo-likelihood estimation for noisy Gaussian Markov random fields. J. Comput. Graph. Statist., 11, 370-388.
    • (2002) J. Comput. Graph. Statist. , vol.11 , pp. 370-388
    • Dryden, I.L.1    Ippoliti, L.2    Romagnoli, L.3
  • 17
    • 0000094018 scopus 로고    scopus 로고
    • Monte Carlo maximum likelihood estimation for non-Gaussian state space models
    • Durbin, J. and Koopman, S. J. (1997) Monte carlo maximum likelihood estimation for non-Gaussian state space models. Biometrika, 84, 669-684.
    • (1997) Biometrika , vol.84 , pp. 669-684
    • Durbin, J.1    Koopman, S.J.2
  • 18
    • 0034354798 scopus 로고    scopus 로고
    • Time series analysis of non-Gaussian observations based on state space models from both classical and Bayesian perspectives
    • Durbin, J. and Koopman, S. J. (2000) Time series analysis of non-Gaussian observations based on state space models from both classical and Bayesian perspectives (with discussion). J. R. Statist. Soc. B, 62, 3-56.
    • (2000) J. R. Statist. Soc. B , vol.62 , pp. 3-56
    • Durbin, J.1    Koopman, S.J.2
  • 19
    • 0035649015 scopus 로고    scopus 로고
    • Bayesian inference for generalized additive mixed models based on Markov random field priors
    • Fahrmeir, L. and Lang, S. (2001a) Bayesian inference for generalized additive mixed models based on Markov random field priors. Appl. Statist., 50, 201-220.
    • (2001) Appl. Statist. , vol.50 , pp. 201-220
    • Fahrmeir, L.1    Lang, S.2
  • 20
    • 0038182874 scopus 로고    scopus 로고
    • Bayesian semiparametric regression analysis of multicategorical time-space data
    • Fahrmeir, L. and Lang, S. (2001b) Bayesian semiparametric regression analysis of multicategorical time-space data. Ann. Inst. Statist. Math., 53, 11-30.
    • (2001) Ann. Inst. Statist. Math. , vol.53 , pp. 11-30
    • Fahrmeir, L.1    Lang, S.2
  • 21
    • 0036434775 scopus 로고    scopus 로고
    • Modelling spatially correlated data via mixtures: A Bayesian approach
    • Fernández, C. and Green, P. J. (2002) Modelling spatially correlated data via mixtures: a Bayesian approach. J. R. Statist. Soc. B, 64, 805-826.
    • (2002) J. R. Statist. Soc. B , vol.64 , pp. 805-826
    • Fernández, C.1    Green, P.J.2
  • 22
    • 84981426681 scopus 로고
    • Data augmentation and dynamic linear models
    • Frühwirth-Schnatter, S. (1994) Data augmentation and dynamic linear models. J. Time Ser. Anal., 15, 183-202.
    • (1994) J. Time Ser. Anal. , vol.15 , pp. 183-202
    • Frühwirth-Schnatter, S.1
  • 23
    • 0001053807 scopus 로고    scopus 로고
    • Markov chain Monte Carlo for dynamic generalised linear models
    • Gamerman, D. (1998) Markov chain Monte Carlo for dynamic generalised linear models. Biometrika, 85, 215-227.
    • (1998) Biometrika , vol.85 , pp. 215-227
    • Gamerman, D.1
  • 24
    • 0037471367 scopus 로고    scopus 로고
    • Space-varying regression models: Specifications and simulations
    • Gamerman, D., Moreira, A. R. B. and Rue, H. (2003) Space-varying regression models: specifications and simulations. Comput. Statist. Data Anal., 42, 513-533.
    • (2003) Comput. Statist. Data Anal. , vol.42 , pp. 513-533
    • Gamerman, D.1    Moreira, A.R.B.2    Rue, H.3
  • 25
    • 0032364029 scopus 로고    scopus 로고
    • Non-parametric Bayesian estimation of a spatial Poisson intensity
    • Heikkinen, J. and Arjas, E. (1998) Non-parametric Bayesian estimation of a spatial Poisson intensity. Scand. J. Statist., 25, 435-450.
    • (1998) Scand. J. Statist. , vol.25 , pp. 435-450
    • Heikkinen, J.1    Arjas, E.2
  • 26
    • 0033240221 scopus 로고    scopus 로고
    • Conditional prior proposals in dynamic models
    • Knorr-Held, L. (1999) Conditional prior proposals in dynamic models. Scand. J. Statist., 26, 129-144.
    • (1999) Scand. J. Statist. , vol.26 , pp. 129-144
    • Knorr-Held, L.1
  • 27
    • 0034665770 scopus 로고    scopus 로고
    • Bayesian modelling of inseparable space-time variation in disease risk
    • Knorr-Held, L. (2000) Bayesian modelling of inseparable space-time variation in disease risk. Statist. Med., 19, 2555-2567.
    • (2000) Statist. Med. , vol.19 , pp. 2555-2567
    • Knorr-Held, L.1
  • 28
    • 0032581956 scopus 로고    scopus 로고
    • Modelling risk from a disease in time and space
    • Knorr-Held, L. and Besag, J. (1998) Modelling risk from a disease in time and space. Statist. Med., 17, 2045-2060.
    • (1998) Statist. Med. , vol.17 , pp. 2045-2060
    • Knorr-Held, L.1    Besag, J.2
  • 29
    • 1642602502 scopus 로고    scopus 로고
    • Bayesian detection of clusters and discontinuities in disease maps
    • Knorr-Held, L. and Raßer, G. (2000) Bayesian detection of clusters and discontinuities in disease maps. Biometrics, 56, 13-21.
    • (2000) Biometrics , vol.56 , pp. 13-21
    • Knorr-Held, L.1    Raßer, G.2
  • 30
    • 0036900109 scopus 로고    scopus 로고
    • On block updating in Markov random field models for disease mapping
    • Knorr-Held, L. and Rue, H. (2002) On block updating in Markov random field models for disease mapping. Scand. J. Statist., 29, 597-614.
    • (2002) Scand. J. Statist. , vol.29 , pp. 597-614
    • Knorr-Held, L.1    Rue, H.2
  • 31
    • 0001789822 scopus 로고
    • Covariance structure of the Gibbs sampler with applications to the comparisons of estimators and augmentation schemes
    • Lui, J. S., Wong, W. H. and Kong, A. (1994) Covariance structure of the Gibbs sampler with applications to the comparisons of estimators and augmentation schemes. Biometrika, 81, 27-40.
    • (1994) Biometrika , vol.81 , pp. 27-40
    • Lui, J.S.1    Wong, W.H.2    Kong, A.3
  • 32
    • 0001595570 scopus 로고
    • Multidimensional multivariate Gaussian Markov random fields with application to image processing
    • Mardia, K. V. (1988) Multidimensional multivariate Gaussian Markov random fields with application to image processing. J. Multiv. Anal., 24, 265-284.
    • (1988) J. Multiv. Anal. , vol.24 , pp. 265-284
    • Mardia, K.V.1
  • 33
    • 0030551974 scopus 로고    scopus 로고
    • Rates of convergence of the Hastings and Metropolis algorithms
    • Mengersen, K. L. and 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.L.1    Tweedie, R.L.2
  • 34
    • 84891435216 scopus 로고    scopus 로고
    • On Metropolis-Hastings algorithms with delayed rejection
    • Mira, A. (2001) On Metropolis-Hastings algorithms with delayed rejection. Metron, 59, 231-241.
    • (2001) Metron , vol.59 , pp. 231-241
    • Mira, A.1
  • 35
    • 0001455988 scopus 로고    scopus 로고
    • Bayesian mapping of disease
    • (eds W. R. Gilks, S. Richardson and D. J. Spiegelhalter). London: Chapman and Hall
    • Mollié, A. (1996) Bayesian mapping of disease. In Markov Chain Monte Carlo in Practice (eds W. R. Gilks, S. Richardson and D. J. Spiegelhalter), pp. 359-379. London: Chapman and Hall.
    • (1996) Markov Chain Monte Carlo in Practice , pp. 359-379
    • Mollié, A.1
  • 36
    • 8644279134 scopus 로고    scopus 로고
    • Discussion on 'Time series analysis of non-Gaussian observations based on state space models from both classical and Bayesian perspectives' (by J. Durbin and S. J. Koopman)
    • Pitt, M. K. (2000) Discussion on 'Time series analysis of non-Gaussian observations based on state space models from both classical and Bayesian perspectives' (by J. Durbin and S. J. Koopman). J. R. Statist. Soc. B, 62, 38-39.
    • (2000) J. R. Statist. Soc. B , vol.62 , pp. 38-39
    • Pitt, M.K.1
  • 38
    • 0040944354 scopus 로고    scopus 로고
    • Markov-chain Monte Carlo: Some practical implications of theoretical results
    • Roberts, G. O. and Rosenthal, J. S. (1998) Markov-chain Monte Carlo: some practical implications of theoretical results (with discussion). Can. J. Statist., 26, 5-31.
    • (1998) Can. J. Statist. , vol.26 , pp. 5-31
    • Roberts, G.O.1    Rosenthal, J.S.2
  • 39
    • 0000051645 scopus 로고    scopus 로고
    • Updating schemes, correlation structure, blocking and parameterization for the Gibbs sampler
    • Roberts, G. O. and Sahu, S. K. (1997) Updating schemes, correlation structure, blocking and parameterization for the Gibbs sampler. J. R. Statist. Soc., B, 59, 291-317.
    • (1997) J. R. Statist. Soc., B , vol.59 , pp. 291-317
    • Roberts, G.O.1    Sahu, S.K.2
  • 40
    • 85132364916 scopus 로고    scopus 로고
    • Exponential convergence of Langevin diffusions and their discrete approximations
    • Roberts, G. O. and Tweedie, R. L. (1996) Exponential convergence of Langevin diffusions and their discrete approximations. Bernoulli, 2, 341-363.
    • (1996) Bernoulli , vol.2 , pp. 341-363
    • Roberts, G.O.1    Tweedie, R.L.2
  • 41
    • 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
  • 42
    • 8644244168 scopus 로고    scopus 로고
    • GMRFLib: A C-library for fast and exact simulation of Gaussian Markov random fields
    • Department of Mathematical Sciences, Norwegian University of Science and Technology, Trondheim
    • Rue, H. and Follestad, T. (2002) GMRFLib: a C-library for fast and exact simulation of Gaussian Markov random fields. Statistics Report 1. Department of Mathematical Sciences, Norwegian University of Science and Technology, Trondheim.
    • (2002) Statistics Report 1
    • Rue, H.1    Follestad, T.2
  • 43
    • 8644237657 scopus 로고    scopus 로고
    • Gaussian markov random field models with applications in spatial statistics
    • Department of Mathematical Sciences, Norwegian University of Science and Technology, Trondheim
    • Rue, H. and Follestad, T. (2003) Gaussian markov random field models with applications in spatial statistics. Statistics Report 6. Department of Mathematical Sciences, Norwegian University of Science and Technology, Trondheim.
    • (2003) Statistics Report 6
    • Rue, H.1    Follestad, T.2
  • 44
    • 0036522614 scopus 로고    scopus 로고
    • Fitting Gaussian Markov random fields to Gaussian fields
    • Rue, H. and Tjelmeland, H. (2002) Fitting Gaussian Markov random fields to Gaussian fields. Scand. J. Statist., 29, 31-50.
    • (2002) Scand. J. Statist. , vol.29 , pp. 31-50
    • Rue, H.1    Tjelmeland, H.2
  • 45
    • 0038853197 scopus 로고
    • Partial non-Gaussian state space
    • Shephard, N. (1994) Partial non-Gaussian state space. Biometrika, 81, 115-131.
    • (1994) Biometrika , vol.81 , pp. 115-131
    • Shephard, N.1
  • 46
    • 0001794777 scopus 로고    scopus 로고
    • Discussion on 'Time series analysis of non-Gaussian observations based on state space models from both classical and Bayesian perspectives' (by J. Durbin and S. J. Koopman)
    • Shephard, N. (2000) Discussion on 'Time series analysis of non-Gaussian observations based on state space models from both classical and Bayesian perspectives' (by J. Durbin and S. J. Koopman). J. R. Statist. Soc. B, 62, 30-32.
    • (2000) J. R. Statist. Soc. B , vol.62 , pp. 30-32
    • Shephard, N.1
  • 47
    • 0003258788 scopus 로고    scopus 로고
    • Likelihood analysis of non-Gaussian measurement time series
    • Shephard, N. and Pitt, M. K. (1997) Likelihood analysis of non-Gaussian measurement time series. Biometrika, 84, 653-667.
    • (1997) Biometrika , vol.84 , pp. 653-667
    • Shephard, N.1    Pitt, M.K.2
  • 48
    • 0001560641 scopus 로고
    • Fully exponential Laplace approximations to expectations and variances of nonpositive functions
    • Tierney, L., Kass, R. E. and Kadane, J. B. (1989) Fully exponential Laplace approximations to expectations and variances of nonpositive functions. J. Am. Statist. Ass., 84, 710-716.
    • (1989) J. Am. Statist. Ass. , vol.84 , pp. 710-716
    • Tierney, L.1    Kass, R.E.2    Kadane, J.B.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.