Bayesian nonstationary spatial modeling for very large datasets

Environmetrics

Volumn 24, Issue 3, 2013, Pages 189-200

  Katzfuss, Matthias ^a  

^a UNIVERSITY OF HEIDELBERG   (Germany)

Author keywords

Covariance tapering; Full scale approximation; Low rank models; Massive datasets; Model selection; Reversible jump MCMC

Indexed keywords

BAYESIAN ANALYSIS; DATA SET; GROUND-BASED MEASUREMENT; INSTRUMENTATION; NUMERICAL MODEL; SATELLITE SENSOR; SOIL ANALYSIS; SPATIAL ANALYSIS; WEATHER STATION;

EID: 84876470895     PISSN: 11804009     EISSN: 1099095X     Source Type: Journal    
DOI: 10.1002/env.2200     Document Type: Article

References (59)

1. Banerjee S, Carlin B, Gelfand AE. 2004. Hierarchical Modeling and Analysis for Spatial Data. Chapman & Hall.
2. Banerjee S, Gelfand AE, Finley AO, Sang H. 2008. Gaussian predictive process models for large spatial data sets. Journal of the Royal Statistical Society, Series B 70(4): 825-848.
3. Berliner LM, Wikle CK, Cressie N. 2000. Long-lead prediction of Pacific SSTs via Bayesian dynamic modeling. Journal of Climate 13(22): 3953-3968.
4. Bevilacqua M, Gaetan C, Mateu J, Porcu E. 2012. Estimating space and space-time covariance functions for large data sets: a weighted composite likelihood approach. Journal of the American Statistical Association 107(497): 268-280.
5. Calder CA. 2007. Dynamic factor process convolution models for multivariate space-time data with application to air quality assessment. Environmental and Ecological Statistics 14(3): 229-247.
6. Cressie N. 1993. Statistics for Spatial Data, Revised Edition. John Wiley & Sons: New York, NY.
7. Cressie N, Johannesson G. 2006. Spatial prediction of massive datasets. In Mastering the Data Explosion in the Earth and Environmental Sciences: Proceedings of the Australian Academy of Science Elizabeth and Frederick White Conference, Canberra, Australia. Australian Academy of Science.
8. Cressie N, Johannesson G. 2008. Fixed rank kriging for very large spatial data sets. Journal of the Royal Statistical Society, Series B 70(1): 209-226.
9. Cressie N, Kang EL. 2010. High-resolution digital soil mapping: kriging for very large datasets. In Proximal Soil Sensing, chapter 4, Viscarra-Rossel R, McBratney A, Minasny B (eds). Springer: Dordrecht, NL; 49-63.
10. Cressie N, Shi T, Kang EL. 2010. Fixed rank filtering for spatio-temporal data. Journal of Computational and Graphical Statistics 19(3): 724-745.
11. Curriero F, Lele S. 1999. A composite likelihood approach to semivariogram estimation. Journal of Agricultural, Biological, and Environmental Statistics 4(1): 9-28.
12. Eidsvik J, Shaby BA, Reich BJ, Wheeler M, Niemi J. 2012. Estimation and prediction in spatial models with block composite likelihoods using parallel computing. Journal of Computational and Graphical Statistics, DOI: 10.1080/10618600.2012.76460, (to appear in print).
13. Finley AO, Sang H, Banerjee S, Gelfand AE. 2009. Improving the performance of predictive process modeling for large datasets. Computational Statistics & Data Analysis 53(8): 2873-2884.
14. Furrer R, Genton MG, Nychka DW. 2006. Covariance tapering for interpolation of large spatial datasets. Journal of Computational and Graphical Statistics 15(3): 502-523.
15. Geman S, Geman D. 1984. Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images. IEEE Transactions on Pattern Analysis and Machine Intelligence 6(6): 721-741.
16. Gilbert JR, Moler C, Schreiber R. 1992. Sparse matrices in MATLAB: design and implementation. SIAM Journal on Matrix Analysis and Applications 13(1): 333-356.
17. Gneiting T. 2002. Compactly supported correlation functions. Journal of Multivariate Analysis 83(2): 493-508.
18. Gneiting T, Raftery AE. 2007. Strictly proper scoring rules, prediction, and estimation. Journal of the American Statistical Association 102(477): 359-378.
19. Green PJ. 1995. Reversible jump Markov chain Monte Carlo computation Bayesian model determination. Biometrika 82(4): 711.
20. Guhaniyogi R, Finley AO, Banerjee S, Gelfand AE. 2011. Adaptive Gaussian predictive process models for large spatial datasets. Environmetrics 22(8): 997-1007.
21. Haario H, Saksman E, Tamminen J. 2001. An adaptive Metropolis algorithm. Bernoulli 7(2): 223-242.
22. Hastings W. 1970. Monte Carlo sampling methods using Markov chains and their applications. Biometrika 57(1): 97-109.
23. Henderson H, Searle S. 1981. On deriving the inverse of a sum of matrices. SIAM Review 23(1): 53-60.
24. Higdon D. 1998. A process-convolution approach to modelling temperatures in the North Atlantic Ocean. Environmental and Ecological Statistics 5(2): 173-190.
25. Holmes C, Mallick B. 2001. Bayesian regression with multivariate linear splines. Journal of the Royal Statistical Society: Series B 63(1): 3-17.
26. Holmes C, Mallick BK. 2000. Bayesian wavelet networks for nonparametric regression. IEEE Transactions on Neural Networks 11(1): 27-35.
27. Kang EL, Cressie N. 2011. Bayesian inference for the spatial random effects model. Journal of the American Statistical Association 106(495): 972-983.
28. Kang EL, Liu D, Cressie N. 2009. Statistical analysis of small-area data based on independence, spatial, non-hierarchical, and hierarchical models. Computational Statistics & Data Analysis 53(8): 3016-3032.
29. Kanter M. 1997. Unimodal spectral windows. Statistics & Probability Letters 34(4): 403-411.
30. Kass R, Raftery A. 1995. Bayes factors. Journal of the American Statistical Association 90(430): 773-795.
31. 2. PhD Dissertation, The Ohio State University, Columbus, OH.
32. Katzfuss M, Cressie N. 2011. Spatio-temporal smoothing and EM estimation for massive remote-sensing data sets. Journal of Time Series Analysis 32(4): 430-446.
33. Katzfuss M, Cressie N. 2012. Bayesian hierarchical spatio-temporal smoothing for very large datasets. Environmetrics 23(1): 94-107.
34. Kaufman C, Schervish M, Nychka DW. 2008. Covariance tapering for likelihood-based estimation in large spatial data sets. Journal of the American Statistical Association 103(484): 1545-1555.
35. Knuth K. 2005. Informed source separation: A Bayesian tutorial. In European signal processing conference, Sanjur B, Cetin E, Tekalp E, Kuruoglu E (eds). Antalya: Turkey.
36. Lemos RT, Sansó B. 2009. A spatio-temporal model for mean, anomaly, and trend fields of North Atlantic sea surface temperature. Journal of the American Statistical Association 104(485): 5-18.
37. Lindgren F, Rue H, Lindström J. 2011. An explicit link between Gaussian fields and Gaussian Markov random fields: the stochastic partial differential equation approach. Journal of the Royal Statistical Society, Series B 73(4): 423-498.
38. Lindsay B. 1988. Composite likelihood methods. In Statistical inference from stochastic processes, Prabhu NU (ed.). RI. American Mathematical Society: Providence; 221-239.
39. Lopes HF, Salazar E, Gamerman D. 2008. Spatial dynamic factor analysis. Bayesian Analysis 3(4): 759-792.
40. Mardia K, Goodall C, Redfern E, Alonso F. 1998. The kriged Kalman filter. Test 7(2): 217-282.
41. Metropolis N, Rosenbluth A, Rosenbluth M, Teller A, Teller E. 1953. Equation of state calculations by fast computing machines. Journal of Chemical Physics 21(6): 1087-1092.
42. Paciorek C, Schervish M. 2006. Spatial modelling using a new class of nonstationary covariance functions. Environmetrics 17(5): 483-506.
43. Pracilio G, Smettem K, Harper R. 2004. New soil survey technologies to map landscape properties relevant to perennial plant performance. In Salinity Solutions, Working with Science and Society, Ridley A, Feikama P, Bennet S, Rogers M-J, Wilkinson R, Hirth J (eds). Bendigo, Victoria: Austalia. Proceedings of the Salinity Solutions Conference.
44. Sang H, Huang JZ. 2012. A full scale approximation of covariance functions. Journal of the Royal Statistical Society, Series B 74(1): 111-132.
45. Sang H, Jun M, Huang JZ. 2011. Covariance approximation for large multivariate spatial datasets with an application to multiple climate model errors. Annals of Applied Statistics 5(4): 2519-2548.
46. Shaby B, Ruppert D. 2012. Tapered covariance: Bayesian estimation and asymptotics. Journal of Computational and Graphical Statistics 21(2): 433-452.
47. Sherman J, Morrison W. 1950. Adjustment of an inverse matrix corresponding to a change in one element of a given matrix. Annals of Mathematical Statistics 21(1): 124-127.
48. Shi T, Cressie N. 2007. Global statistical analysis of MISR aerosol data: a massive data product from NASA's Terra satellite. Environmetrics 18: 665-680.
49. Stein ML. 1999. Interpolation of Spatial Data: Some Theory for Kriging. Springer: New York, NY.
50. Stein ML. 2005. Nonstationary spatial covariance functions. Technical Report Technical Report No. 21, Center for Integrating Statistical and Environmental Science, The University of Chicago, Chicago, IL.
51. Stein ML. 2008. A modeling approach for large spatial datasets. Journal of the Korean Statistical Society 37(1): 3-10.
52. Taylor M, Smettem K, Pracilio G, Verboom W. 2002. Relationships between soil properties and high-resolution radiometrics, central eastern Wheatbelt, Western Australia. Exploration Geophysics 33(2): 95-102.
53. van Dyk DA, Park T. 2008. Partially collapsed Gibbs samplers: theory and methods. Journal of the American Statistical Association 103: 790-796.
54. Viscarra Rossel R, Taylor HJ, McBratney A. 2007. Multivariate calibration of hyperspectral γ-ray energy spectra for proximal soil sensing. European Journal of Soil Science 58(1): 343-353.
55. Wikle CK. 2010. Low-rank representations for spatial processes. In Handbook of Spatial Statistics, Gelfand AE, Fuentes M, Guttorp P, Diggle P (eds). Chapman and Hall/CRC: Boca Raton, FL; 107-118.
56. Wikle CK, Cressie N. 1999. A dimension-reduced approach to space-time Kalman filtering. Biometrika 86(4): 815-829.
57. Wikle CK, Milliff R, Nychka DW, Berliner LM. 2001. Spatiotemporal hierarchical Bayesian modeling: tropical ocean surface winds. Journal of the American Statistical Association 96(454): 382-397.
58. Woodbury M. 1950. Inverting modified matrices. Technical Report Memorandum Report 42, Statistical Research Group, Princeton University, Princeton, NJ.
59. Xu B, Wikle CK, Fox N. 2005. A kernel-based spatio-temporal dynamical model for nowcasting radar precipitation. Journal of the American Statistical Association 100(472): 1133-1144.