Bivariate geostatistical modelling: A review and an application to spatial variation in radon concentrations

Environmental and Ecological Statistics

Volumn 19, Issue 2, 2012, Pages 139-160

  Fanshawe, Thomas R ^a   Diggle, Peter J ^a  

^a LANCASTER UNIVERSITY   (United Kingdom)

Author keywords

Common component model; Kernel convolution; Linear model of coregionalisation

Indexed keywords

CALCIUM; GEOSTATISTICS; MAGNESIUM; MODELING; RADON; SOIL CHEMISTRY; SPATIAL VARIATION;

CANADA; MANITOBA; WINNIPEG;

EID: 84862673322     PISSN: 13528505     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10651-011-0179-7     Document Type: Article

References (61)

1. Banerjee S, Gelfand A, Finley A, Sang H (2008) Gaussian predictive process models for large spatial data sets. J Roy Stat Soc B 70: 825-848.
2. Bárdossy A (2006) Copula-based geostatistical models for groundwater quality parameters. Water Resour Res 42: w11416. doi: 10. 1029/2005WR004754.
3. Bárdossy A, Li J (2008) Geostatistical interpolation using copulas. Water Resour Res 44: w07412. doi: 10. 1029/2007WR006115.
4. Barry R, Ver Hoef J (1996) Blackbox kriging: spatial prediction without specifying variogram models. J Agric Biol Environ Stat 1: 297-322.
5. Berliner L (2000) Hierarchical Bayesian modeling in the environmental sciences. Allgemeines Statistische Archiv 84: 141-153.
6. Boyle P, Frean M (2005) Multiple output Gaussian process regression. Tech. rep., School of Mathematical and Computing Sciences, Victoria University of Wellington.
7. Brabec M, Jílek K (2009) Dynamical model for indoor radon concentration monitoring. Environmetrics 20: 718-729.
8. Calder C (2007) Dynamic factor process convolution models for multivariate space-time data with application to air quality assessment. Environ Ecol Stat 14: 229-247.
9. Calder C (2008) A dynamic process convolution approach to modeling ambient particulate matter concentrations. Environmetrics 19: 39-48.
10. Calder C, Cressie N (2007) Some topics in convolution-based spatial modeling. In: Proceedings of the 56th session of the international statistics institute, Lisbon, Portugal.
11. Calder C, Craigmile P, Zhang J (2009) Regional spatial modelling of topsoil geochemistry. Biometrics 65: 206-215.
12. Chilès JP, Delfiner P (1999) Geostatistics: modeling spatial uncertainty. Wiley, New York.
13. Cressie N (1993) Statistics for spatial data. Wiley, New York.
14. Cressie N, Wikle C (1998) The variance-based cross-variogram: you can add apples and oranges. Math Geol 30: 789-799.
15. D'Agostino V, Greene E, Passarella G, Vurro M (1993) Spatial and temporal study of nitrate concentration in groundwater by means of coregionalization. Environ Geol 36: 285-295.
16. Diggle P, Ribeiro Jr P (2007) Model-based geostatistics. Springer, New York.
17. Frees E, Valdez E (1998) Understanding relationships using copulas. North Am Actuar J 2: 1-25.
18. Fuentes M (2001) A high frequency kriging approach for nonstationary environmental processes. Environmetrics 12: 469-483.
19. Fuentes M (2002) Interpolation of nonstationary air pollution processes: a spatial spectral approach. Stat Modell 2: 281-298.
20. Fuentes M (2002) Spectral methods for nonstationary spatial processes. Biometrika 89: 197-210.
21. Gelfand A, Schmidt A, Sirmans C (2003) Multivariate spatial process models: conditional and unconditional Bayesian approaches using coregionalization. Tech. rep., Institute of Statistics and Decision Sciences, Duke University.
22. Goovaerts P (1994) On a controversial method for modeling a coregionalization. Math Geol 26: 197-204.
23. Goulard M, Voltz M (1992) Linear coregionalization model: tools for estimation and choice of cross-variogram matrix. Math Geol 24: 269-286.
24. Haas T (1996) Multivariate spatial prediction in the presence of non-linear trend and covariance non-stationarity. Environmetrics 7: 145-165.
25. Higdon D (1998) A process-convolution approach to modelling temperatures in the North Atlantic Ocean. Environ Ecol Stat 5: 173-190.
26. Higdon D (2002) Space and space-time modeling using process convolutions. In: Anderson C, Barnett V, Chatwin P, El-Shaarawi A (eds) Quantitative methods for current environmental issues. Springer, New York, pp 37-56.
27. Hunter N, Muirhead C, Miles J, Appleton J (2009) Uncertainties in radon related to house-specific factors and proximity to geological boundaries in England. Radiat Prot Dosim 136: 17-22.
28. Jenkins G, Watts D (1968) Spectral analysis and its applications. Holden-Day, San Francisco.
29. Kern J (2000) Bayesian process-convolution approaches to specifying spatial dependence structure. PhD thesis, Duke University.
30. Knorr-Held L, Best N (2001) A shared component model for detecting joint and selective clustering of two diseases. J Roy Stat Soc A 164: 73-85.
31. Krewski D, Lubin J, Zielinski J, Alavanja M, Catalan V, Field R, Klotz J, Létourneau E, Lynch C, Lyon J, Sandler D, Schoenberg J, Steck D, Stolwijk J, Weinberg C, Wilcox H (2006) A combined analysis of North American case-control studies of residential radon and lung cancer. J Toxicol Environ Health Part A Curr Issues 69: 533-597.
32. Lark R (2002) Robust estimation of the pseudo cross-variogram for cokriging soil properties. Eur J Soil Sci 53: 253-270.
33. Lark R (2003) Two robust estimators of the cross-variogram for multivariate geostatistical analysis of soil properties. Eur J Soil Sci 54: 187-201.
34. Lee H, Higdon D, Calder C, Holloman C (2005) Efficient models for correlated data via convolutions of intrinsic processes. Stat Model 5: 53-74.
35. Létourneau E, Zielinski J, Krewski D, McGregor R (1992) Levels of radon gas in Winnipeg homes. Radiat Prot Dosim 45: 531-534.
36. Létourneau E, Krewski D, Choi N, Goddard M, McGregor R, Zielinski J, Du J (1994) Case-control study of residential radon and lung cancer in Winnipeg, Manitoba, Canada. Am J Epidemiol 140: 310-322.
37. Li B, Genton M, Sherman M (2008) Testing the covariance structure of multivariate random fields. Biometrika 95: 813-829.
38. Majumdar A, Gelfand A (2007) Multivariate spatial modeling for geostatistical data using convolved covariance functions. Math Geol 39: 225-245.
39. Majumdar A, Paul D, Bautista D (2007) A generalized convolution model for multivariate nonstationary spatial processes. Tech. rep., Department of Mathematics and Statistics, Arizona State University.
40. Marchant B, Lark R (2007) Estimation of linear models of coregionalization by residual maximum likelihood. Eur J Soil Sci 58: 1506-1513.
41. Mardia K, Goodall C (1993) Spatial-temporal analysis of multivariate environmental monitoring data. In: Patil G, Rao C (eds) Multivariate environmental statistics. North-Holland, Amsterdam, pp 347-386.
42. Nychka D, Saltzman N (1998) Design of air-quality monitoring networks. In: Nychka D, Piegorsch W, Cox L (eds) Case studies in Environmental Statistics. Springer, New York, Chap 4, pp 51-76.
43. Oliver D (2003) Gaussian cosimulation: modelling of the cross-covariance. Math Geol 35: 681-698.
44. Priestley M (1981) Spectral analysis and time series. Academic Press, New York.
45. R Development Core Team (2008) R: a language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria, URL http://www. R-project. org, ISBN 3-900051-07-0.
46. Ribeiro Jr P, Diggle P (2001) geoR: a package for geostatistical analysis. R-NEWS 1(2): 14-18, URL http://CRAN. R-project. org/doc/Rnews/, ISSN 1609-3631.
47. Rodrigues A, Diggle P (2010) A class of convolution-based models for spatio-temporal processes with non-separable covariance structure. Scand J Stat 37: 553-567.
48. Royle J, Berliner L (1999) A hierarchical approach to multivariate spatial modeling and prediction. J Agric Biol and Environ Stat 4: 29-56.
49. Rue H, Tjelmeland H (2002) Fitting Gaussian Markov random fields to Gaussian fields. Scand J Stat 29: 31-49.
50. Schmidt A, Gelfand A (2003) A Bayesian coregionalization approach for multivariate pollution data. J Geophy Res Atmos 108(D24): 8783.
51. Steck D, Field R, Lynch C (1999) Exposure to atmospheric radon. Environ Heal Perspect 107: 123-127.
52. Stroud J, Müller P, Sansó B (2001) Dynamic models for spatiotemporal data. J Roy Stat Soc B 63: 673-689.
53. Ver Hoef J, Barry R (1998) Constructing and fitting models for cokriging and multivariable spatial prediction. J Stat Plan Inference 69: 275-294.
54. Ver Hoef J, Cressie N (1993) Multivariable spatial prediction. Math Geol 25: 219-240.
55. Ver Hoef J, Cressie N, Barry R (2004) Flexible spatial models for kriging and cokriging using moving averages and the fast fourier transform (fft). J Comput Graph Stat 13: 265-282.
56. Wackernagel H (1995) Multivariate geostatistics. Springer, Berlin.
57. Whitley E, Darby S (1999) Quantifying the risks from residential radon. In: Barnett V, Stein A, Feridun Turkman K (eds) Statistical aspects of health and the environment. Wiley, Chichester, chap 5, pp 73-89.
58. Xia G, Gelfand A (2005) Stationary process approximation for the analysis of large spatial datasets. Tech. rep., Institute of Statistics and Decision Sciences, Duke University.
59. Yaglom A (2004) An introduction to the theory of stationary random functions. Dover, Mineola.
60. Zhang H (2004) Inconsistent estimation and asymptopically equal interpolations in model-based geostatistics. J Am Stat Assoc 99: 250-261.
61. Zhang H (2007) Maximum-likelihood estimation for multivariate spatial linear coregionalization models. Environmetrics 18: 125-139.