메뉴 건너뛰기




Volumn 29, Issue 15, 2010, Pages 1580-1607

Approximate inference for disease mapping with sparse Gaussian processes

Author keywords

Compact support covariance; Expectation propagation; Laplace approximation; Sparse Gaussian process

Indexed keywords

ALCOHOLISM; ARTICLE; COMPUTATIONAL FLUID DYNAMICS; CONTROLLED STUDY; COVARIANCE; DISEASE COURSE; EXPECTATION PROPAGATION ALGORITHM; FUZZY SYSTEM; KERNEL METHOD; LAPLACE APPROXIMATION; LEARNING ALGORITHM; MACHINE LEARNING; MONTE CARLO METHOD; PROBABILITY; RISK FACTOR; SPATIAL AUTOCORRELATION ANALYSIS; STATISTICAL DISTRIBUTION; STOCHASTIC MODEL; THEORETICAL MODEL;

EID: 77953768713     PISSN: 02776715     EISSN: 10970258     Source Type: Journal    
DOI: 10.1002/sim.3895     Document Type: Article
Times cited : (61)

References (62)
  • 3
    • 25444528713 scopus 로고    scopus 로고
    • Assessing approximate inference for binary Gaussian process classification
    • Kuss M, Rasmussen CE. Assessing approximate inference for binary Gaussian process classification. Journal of Machine Learning Research 2005; 6:1679-1704.
    • (2005) Journal of Machine Learning Research , vol.6 , pp. 1679-1704
    • Kuss, M.1    Rasmussen, C.E.2
  • 4
    • 84864038646 scopus 로고    scopus 로고
    • Sparse Gaussian process using pseudo-inputs
    • Weiss Y, Schölkopf B, Platt J (eds). The MIT Press: Cambridge, MA
    • Snelson E, Ghahramani Z. Sparse Gaussian process using pseudo-inputs. In Advances in Neural Information Processing Systems 18, Weiss Y, Schölkopf B, Platt J (eds). The MIT Press: Cambridge, MA, 2006.
    • (2006) Advances in Neural Information Processing Systems 18
    • Snelson, E.1    Ghahramani, Z.2
  • 5
    • 29144453489 scopus 로고    scopus 로고
    • A unifying view of sparse approximate Gaussian process regression
    • Quiñonero-Candela J, Rasmussen CE. A unifying view of sparse approximate Gaussian process regression. Journal of Machine Learning Research 2005; 6(3):1939-1959. (Pubitemid 41798128)
    • (2005) Journal of Machine Learning Research , vol.6 , pp. 1939-1959
    • Quinonero-Candela, J.1    Rasmussen, C.E.2
  • 11
    • 12744255376 scopus 로고    scopus 로고
    • A comparison of Bayesian spatial models for disease mapping
    • DOI: 10.1191/0962280205sm388oa
    • Best N, Richardson S, Thomson A. A comparison of Bayesian spatial models for disease mapping. Statistical Methods in Medical Research 2005; 14:35-59. DOI: 10.1191/0962280205sm388oa.
    • (2005) Statistical Methods in Medical Research , vol.14 , pp. 35-59
    • Best, N.1    Richardson, S.2    Thomson, A.3
  • 12
    • 0003564226 scopus 로고    scopus 로고
    • Elliot P, Wakefield J, Best N, Briggs D (eds). Oxford University Press: Oxford
    • Elliot P, Wakefield J, Best N, Briggs D (eds). Spatial Epidemiology Methods and Applications. Oxford University Press: Oxford, 2001.
    • (2001) Spatial Epidemiology Methods and Applications
  • 13
    • 62849120031 scopus 로고    scopus 로고
    • Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations
    • DOI: 10.1111/j.1467-9868.2008.00700.x
    • Rue H, Martino S, Chopin N. Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations. Journal of Royal Statistical Society B 2009; 71(2):1-35. DOI: 10.1111/j.1467-9868.2008. 00700.x.
    • (2009) Journal of Royal Statistical Society B , vol.71 , Issue.2 , pp. 1-35
    • Rue, H.1    Martino, S.2    Chopin, N.3
  • 14
    • 0038891993 scopus 로고    scopus 로고
    • Sparse online Gaussian processes
    • DOI: 10.1162/089976602317250933
    • Csató L, Opper M. Sparse online Gaussian processes. Neural Computation 2002; 14(3):641-669. DOI: 10.1162/089976602317250933.
    • (2002) Neural Computation , vol.14 , Issue.3 , pp. 641-669
    • Csató, L.1    Opper, M.2
  • 15
    • 33745987673 scopus 로고    scopus 로고
    • Fast forward selection to speed up sparse Gaussian process regression
    • Bishop CM, Frey BJ (eds). Society for Artificial Intelligence and Statistics: New Jersey, U.S.A.
    • Seeger M, Williams CKI, Lawrence N. Fast forward selection to speed up sparse Gaussian process regression. In Ninth International Workshop on Artificial Intelligence and Statistics, Bishop CM, Frey BJ (eds). Society for Artificial Intelligence and Statistics: New Jersey, U.S.A., 2003.
    • (2003) Ninth International Workshop on Artificial Intelligence and Statistics
    • Seeger, M.1    Williams, C.K.I.2    Lawrence, N.3
  • 16
    • 0000414912 scopus 로고    scopus 로고
    • A dimension-reduced approach to space-time Kalman filtering
    • DOI: 10.1093/biomet/86.4.815
    • Wikle CK, Cressie N. A dimension-reduced approach to space-time Kalman filtering. Biometrica 1999; 86:815-829. DOI: 10.1093/biomet/86.4.815.
    • (1999) Biometrica , vol.86 , pp. 815-829
    • Wikle, C.K.1    Cressie, N.2
  • 17
    • 17344370420 scopus 로고    scopus 로고
    • Sequential, Bayesian geostatistics: A principle method for large data sets
    • DOI: 10.1111/j.1538-4632.2005.00635.x
    • Cornford D, Csató L, Opper M. Sequential, Bayesian geostatistics: a principle method for large data sets. Geographical Analysis 2005; 37:183-199. DOI: 10.1111/j.1538-4632.2005.00635.x.
    • (2005) Geographical Analysis , vol.37 , pp. 183-199
    • Cornford, D.1    Csató, L.2    Opper, M.3
  • 18
    • 33947661458 scopus 로고    scopus 로고
    • Computational techniques for spatial logistic regression with large datasets
    • DOI: 10.1016/j.csda.2006.11.008
    • Paciorek CJ. Computational techniques for spatial logistic regression with large datasets. Computational Statistics and Data Analysis 2007;51:3631-3653. DOI: 10.1016/j.csda.2006.11.008.
    • (2007) Computational Statistics and Data Analysis , vol.51 , pp. 3631-3653
    • Paciorek, C.J.1
  • 19
    • 47649103974 scopus 로고    scopus 로고
    • Gaussian predictive process models for large spatial data sets
    • DOI: 10.1111/j.1467-9868.2008.00663.x
    • Banerjee S, Gelfand AE, Finley AO, Sang H. Gaussian predictive process models for large spatial data sets. Journal of Royal statistical Society B 2008; 70(4):825-848. DOI: 10.1111/j.1467-9868.2008.00663.x.
    • (2008) Journal of Royal Statistical Society B , vol.70 , Issue.4 , pp. 825-848
    • Banerjee, S.1    Gelfand, A.E.2    Finley, A.O.3    Sang, H.4
  • 27
    • 0036858503 scopus 로고    scopus 로고
    • Compactly supported correlation functions
    • DOI: 10.1006/jmva.2001.2056
    • Gneiting T. Compactly supported correlation functions. Journal of Multivariate Analysis 2002; 83:493-508. DOI: 10.1006/jmva.2001.2056.
    • (2002) Journal of Multivariate Analysis , vol.83 , pp. 493-508
    • Gneiting, T.1
  • 28
    • 84867086419 scopus 로고    scopus 로고
    • Prior distributions for variance parameters in hierarchical models
    • DOI: 10.1214/06-BA117A
    • Gelman A. Prior distributions for variance parameters in hierarchical models. Bayesian Analysis 2006; 1(3):515-533. DOI: 10.1214/06-BA117A.
    • (2006) Bayesian Analysis , vol.1 , Issue.3 , pp. 515-533
    • Gelman, A.1
  • 30
    • 43449137394 scopus 로고    scopus 로고
    • Technical Report, Max Planck Institute for Biological Cybernetics, Tübingen, Germany
    • Seeger M. Expectation propagation for exponential families. Technical Report, Max Planck Institute for Biological Cybernetics, Tübingen, Germany, 2005.
    • (2005) Expectation Propagation for Exponential Families
    • Seeger, M.1
  • 31
    • 84862617524 scopus 로고    scopus 로고
    • Gaussian quadrature based expectation propagation
    • Cowell RG, Ghahramani Z (eds). Society for Artificial Intelligence and Statistics: New Jersey, U.S.A.
    • Zoeter O, Heskes T. Gaussian quadrature based expectation propagation. In Proceedings of the Ninth International Workshop on Artificial Intelligence and Statistics, Cowell RG, Ghahramani Z (eds). Society for Artificial Intelligence and Statistics: New Jersey, U.S.A., 2005; 445-452.
    • (2005) Proceedings of the Ninth International Workshop on Artificial Intelligence and Statistics , pp. 445-452
    • Zoeter, O.1    Heskes, T.2
  • 32
    • 35548979581 scopus 로고    scopus 로고
    • Vectorized adaptive quadrature in MATLAB
    • DOI: 10.1016/j.cam.2006.11.021
    • Shampine LF. Vectorized adaptive quadrature in MATLAB. Journal of Computational and Applied Mathematics 2008; 211:131-140. DOI: 10.1016/j.cam.2006.11.021.
    • (2008) Journal of Computational and Applied Mathematics , vol.211 , pp. 131-140
    • Shampine, L.F.1
  • 36
    • 0001667705 scopus 로고
    • Bayesian inference in econometric models using Monte Carlo integration
    • Geweke J. Bayesian inference in econometric models using Monte Carlo integration. Econometrica 1989; 57(6):721-741.
    • (1989) Econometrica , vol.57 , Issue.6 , pp. 721-741
    • Geweke, J.1
  • 38
    • 84893792941 scopus 로고
    • Monte Carlo methods for solving multivariate problems
    • DOI: 10.1111/j.1749-6632.1960.tb42846.x
    • Hammersley JM. Monte Carlo methods for solving multivariate problems. Annals of the New York Academy of Sciences 1960; 86(3):844-874. DOI: 10.1111/j.1749-6632.1960.tb42846.x.
    • (1960) Annals of the New York Academy of Sciences , vol.86 , Issue.3 , pp. 844-874
    • Hammersley, J.M.1
  • 39
    • 33745285728 scopus 로고    scopus 로고
    • Very large fractional factorials and central composite designs
    • DOI: 10.1145/1113316.1113320
    • Sanchez SM, Sanchez PJ. Very large fractional factorials and central composite designs. ACM Transactions on Modeling and Computer Simulation 2005; 15:362-377. DOI: 10.1145/1113316.1113320.
    • (2005) ACM Transactions on Modeling and Computer Simulation , vol.15 , pp. 362-377
    • Sanchez, S.M.1    Sanchez, P.J.2
  • 41
  • 43
    • 67650493910 scopus 로고    scopus 로고
    • Perturbation corrections in approximate inference: Mixture modelling applications
    • Paquet U, Winther O, Opper M. Perturbation corrections in approximate inference: mixture modelling applications. Journal of Machine Learning Research 2009; 10:1263-1304.
    • (2009) Journal of Machine Learning Research , vol.10 , pp. 1263-1304
    • Paquet, U.1    Winther, O.2    Opper, M.3
  • 47
    • 85162029278 scopus 로고    scopus 로고
    • The generalized FITC approximation
    • Platt J, Koller D, Singer Y, Roweis S (eds). MIT Press: Cambridge, MA
    • Naish-Guzman A, Holden S. The generalized FITC approximation. In Advances in Neural Information Processing Systems 20, Platt J, Koller D, Singer Y, Roweis S (eds). MIT Press: Cambridge, MA, 2008.
    • (2008) Advances in Neural Information Processing Systems 20
    • Naish-Guzman, A.1    Holden, S.2
  • 48
    • 2942699190 scopus 로고    scopus 로고
    • Algorithm 837: AMD, an approximate minimum degree ordering algorithm
    • DOI: 10.1145/1024074.1024081
    • Amestoy P, Davis TA, Duff IS. Algorithm 837: AMD, an approximate minimum degree ordering algorithm. ACM Transactions on Mathematical Software 2004; 30(3):381-388. DOI: 10.1145/1024074.1024081.
    • (2004) ACM Transactions on Mathematical Software , vol.30 , Issue.3 , pp. 381-388
    • Amestoy, P.1    Davis, T.A.2    Duff, I.S.3
  • 50
    • 0008452761 scopus 로고
    • Formation of a sparse bus impedance matrix and its application to short circuit study
    • IEEE Power Engineering Society: Minneapolis, U.S.A.
    • Takahashi K, Fagan J, Chen MS. Formation of a sparse bus impedance matrix and its application to short circuit study. Power Industry Computer Application Conference Proceedings. IEEE Power Engineering Society: Minneapolis, U.S.A., 1973.
    • (1973) Power Industry Computer Application Conference Proceedings
    • Takahashi, K.1    Fagan, J.2    Chen, M.S.3
  • 52
    • 34250219986 scopus 로고    scopus 로고
    • Approximate Bayesian inference for hierarchical Gaussian Markov random field models
    • DOI: 10.1016/j.jspi.2006.07.016
    • Rue H, Martino S. Approximate Bayesian inference for hierarchical Gaussian Markov random field models. Journal of Statistical Planning and Inference 2007; 137:3177-3192. DOI: 10.1016/j.jspi.2006.07.016.
    • (2007) Journal of Statistical Planning and Inference , vol.137 , pp. 3177-3192
    • Rue, H.1    Martino, S.2
  • 53
    • 22944441327 scopus 로고    scopus 로고
    • Row modifications of a sparse Cholesky factorization
    • DOI: 10.1137/S089547980343641X
    • Davis TA, Hager WW. Row modifications of a sparse Cholesky factorization. SIAM Journal on Matrix Analysis and Applications 2005; 26(3):621-639. DOI: 10.1137/S089547980343641X.
    • (2005) SIAM Journal on Matrix Analysis and Applications , vol.26 , Issue.3 , pp. 621-639
    • Davis, T.A.1    Hager, W.W.2
  • 54
    • 0040946757 scopus 로고
    • Incomplete nested dissection for solving n by n grid problems
    • DOI: 10.1137/0715044
    • George A, William G, Poole J, Voigt RG. Incomplete nested dissection for solving n by n grid problems. SIAM Journal on Numerical Analysis 1978; 15(4):662-673. DOI: 10.1137/0715044.
    • (1978) SIAM Journal on Numerical Analysis , vol.15 , Issue.4 , pp. 662-673
    • George, A.1    William, G.2    Poole, J.3    Voigt, R.G.4
  • 56
    • 0032273615 scopus 로고    scopus 로고
    • General methods for monitoring convergence of iterative simulations
    • Brooks SP, Gelman A. General methods for monitoring convergence of iterative simulations. Journal of Computational and Graphical Statistics 1998; 7(4):434-455. (Pubitemid 128635035)
    • (1998) Journal of Computational and Graphical Statistics , vol.7 , Issue.4 , pp. 434-455
    • Brooks, S.P.1    Gelman, A.2
  • 58
    • 84972511893 scopus 로고
    • Practical Markov chain Monte Carlo
    • DOI: 10.1214/ss/1177011137
    • Geyer CJ. Practical Markov chain Monte Carlo. Statistical Science 1992; 7(4):473-511. DOI: 10.1214/ss/1177011137.
    • (1992) Statistical Science , vol.7 , Issue.4 , pp. 473-511
    • Geyer, C.J.1
  • 59
    • 0000273048 scopus 로고    scopus 로고
    • Annealed importance sampling
    • DOI: 10.1023/A:1008923215028
    • Neal RM. Annealed importance sampling. Statistics and Computing 2001; 11:125-139. DOI: 10.1023/A:1008923215028.
    • (2001) Statistics and Computing , vol.11 , pp. 125-139
    • Neal, R.M.1
  • 60
    • 0036781790 scopus 로고    scopus 로고
    • Bayesian model assessment and comparison using cross-validation predictive densities
    • Vehtari A, Lampinen J. Bayesian model assessment and comparison using cross-validation predictive densities. Neural Computation 2002;14(10):2439-2468.
    • (2002) Neural Computation , vol.14 , Issue.10 , pp. 2439-2468
    • Vehtari, A.1    Lampinen, J.2
  • 61
    • 0000079228 scopus 로고
    • Model determination using predictive distributions with implementation via sampling-based methods (with Discussion)
    • Bernardo JM, Berger JO, Dawid AP, Smith AFM (eds). Oxford University Press: Oxford
    • Gelfand AE, Dey DK, Chang H. Model determination using predictive distributions with implementation via sampling-based methods (with Discussion). In Bayesian Statistics 4, Bernardo JM, Berger JO, Dawid AP, Smith AFM (eds). Oxford University Press: Oxford, 1992; 147-167.
    • (1992) Bayesian Statistics 4 , pp. 147-167
    • Gelfand, A.E.1    Dey, D.K.2    Chang, H.3
  • 62
    • 2142734871 scopus 로고    scopus 로고
    • Inconsistent Estimation and Asymptotically Equal Interpolations in Model-Based Geostatistics
    • Zhang H. Inconsistent estimation and asymptotically equal interpolations in model-based geostatistics. Journal of the American Statistical Association 2004; 99(465):250-261. DOI: 10.1198/016214504000000241. (Pubitemid 38545211)
    • (2004) Journal of the American Statistical Association , vol.99 , Issue.465 , pp. 250-261
    • Zhang, H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.