Model-based geostatistics

Journal of the Royal Statistical Society. Series C: Applied Statistics

Volumn 47, Issue 3, 1998, Pages 299-350

  Diggle, P J ^a   Tawn, J A ^b   Moyeed, R A ^b  

^a LANCASTER UNIVERSITY   (United Kingdom)

^b NONE

Author keywords

Generalized linear mixed model; Geostatistics; Kriging; Markov chain Monte Carlo method; Spatial prediction

Indexed keywords

EID: 0040843494     PISSN: 00359254     EISSN: None     Source Type: Journal    
DOI: 10.1111/1467-9876.00113     Document Type: Article

References (39)

1. Armstrong, M. and Matheron, G. (1986a) Disjunctive kriging revisited: part I. Math. Geol., 18, 711-728.
2. _(1986b) Disjunctive kriging revisited: part II. Math. Geol., 18, 729-742.
3. Besag, J. and Green, P. J. (1993) Spatial statistics and Bayesian computation. J. R. Statist. Soc. B, 55, 25-37.
4. 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.
5. Breslow, N. E. and Clayton, D. G. (1993) Approximate inference in generalized linear mixed models. J. Am. Statist. Ass., 88, 9-25.
6. Clayton, D. G. and Kaldor, J. (1987) Empirical Bayes estimates of age-standardized relative risks for use in disease mapping. Biometrics, 43, 671-681.
7. Cowles, M. K. and Carlin, B. P. (1996) Markov chain Monte Carlo convergence diagnostics: a comparative review. J. Am. Statist. Ass., 91, 883-904.
8. Cressie, N. (1985) Fitting variogram models by weighted least squares. J. Int. Ass. Math. Geol., 17, 563-586.
9. _(1991) Statistics for Spatial Data. New York: Wiley.
10. _(1994) Comment on the paper by Handcock and Wallis. J. Am. Statist. Ass., 89, 379-382.
11. Diggle, P. J., Harper, L. and Simon, S. (1997) A geostatistical analysis of residual contamination from nuclear weapons testing. In Statistics for the Environment 3 (eds V. Barnett and K. F. Turkman), pp. 89-107. Chichester: Wiley.
12. Diggle, P. J., Liang, K.-Y. and Zeger, S. L. (1994) The Analysis of Longitudinal Data. Oxford: Clarendon.
13. Freulon, X. (1994) Conditional simulation of a Gaussian random vector with non linear and/or noisy observations. In Geostatistical Simulations (eds M. Armstrong and P. A. Dowd), pp. 57-71. Dordrecht: Kluwer.
14. Gilks, W. R., Clayton, D. G., Spiegelhalter, D. J., Best, N. G., McNeil, A. J., Sharples, L. D. and Kirby, A. J. (1993) Modelling complexity: applications of Gibbs sampling in medicine. J. R. Statist. Soc. B, 55, 39-52.
15. Gilks, W. R. and Wild, P. (1992) Adaptive rejection sampling for Gibbs sampling. Appl. Statist., 41, 337-348.
16. Handcock, M. S. and Stein, M. L. (1993) A Bayesian analysis of kriging. Technometrics, 35, 403-410.
17. Handcock, M. S. and Wallis, J. R. (1994) An approach to statistical spatial-temporal modelling of meteorological fields. J. Am. Statist. Ass., 89, 368-390.
18. Isaaks, E. H. and Srivastava, R. M. (1989) An Introduction to Applied Geostatistics. Oxford: Oxford University Press.
19. Jones, K. and Telford, D. (1991) On the trail of a seasonal microbe. New Scient., Apr. 6th, 36-39.
20. Journel, A. G. (1983) Nonparametric estimation of spatial distributions. J. Int. Ass. Math. Geol., 9, 563-586.
21. Journel, A. G. and Huijbregts, C. J. (1978) Mining Geostatistics. London: Academic Press.
22. Laslett, G. M. (1994) Kriging and splines: an empirical comparison of their predictive performance in some applications (with discussion). J. Am. Statist. Ass., 89, 391-409.
23. Lawson, A. B., Biggeri, A. and Lagazio, C. (1996) Modelling heterogeneity in discrete spatial data models via MAP and MCMC methods. In Proc. 11th Int. Wrkshp Statistical Modelling (eds A. Forcina, G. M. Marchetti, R. Hatzinger and G. Galmacci), pp. 240-250. Citta di Castello: Graphos.
24. Le, N. D. and Zidek, J. V. (1992) Interpolation with uncertain spatial covariances: a Bayesian alternative to kriging. J. Multiv. Anal., 43, 351-374.
25. Lindgren, G. and Rychlik, I. (1994) How reliable are contour curves - confidence sets for level contours. Technical Report 3102. University of Lund, Lund.
26. Mardia, K. V., Kent, J. T. and Bibby, J. M. (1979) Multivariate Analysis. London: Academic Press.
27. Mardia, K. V. and Marshall, R. J. (1984) Maximum likelihood estimation of models for residual covariance in spatial regression. Biometrika, 72, 135-146.
28. Mardia, K. V. and Watkins, A. J. (1989) On multimodality of the likelihood in the spatial linear model. Biometrika, 76, 289-295.
29. Matérn, B. (1960) Spatial variation. Report. Statens Skogsforsningsinstitut, Stockholm.
30. Matheron, G. (1970) The theory of regionalized variables and its applications. Cah. Centr. Morph. Math. Fontainebleau, no. 5.
31. _(1976) A simple substitute for conditional expectation: the disjunctive kriging. In Advanced Geostatistics in the Mining Industry (eds M. Guarascio, M. David and C. Huijbregts), pp. 221-236. Dordrecht: Reidel.
32. McCullagh, P. and Nelder, J. A. (1989) Generalized Linear Models, 2nd edn. London: Chapman and Hall.
33. 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.
34. Nelder, J. A. and Wedderburn, R. W. M. (1972) Generalized linear models. J. R. Statist. Soc. A, 135, 370-384.
35. Papritz, A. and Moyeed, R. A. (1997) Empirical validation of linear and nonlinear methods for spatial point prediction. Technical Report. Institute of Terrestrial Ecology, Eidgenössiche Technische Hochschule, Zurich.
36. Raftery, A. E. and Banfield, J. D. (1991) Stopping the Gibbs sampler, the use of morphology, and other issues in spatial statistics. Ann. Inst. Statist. Math., 43, 32-43.
37. Ripley, B. D. (1981) Spatial Statistics. New York: Wiley.
38. Smith, A. F. M. and Roberts, G. O. (1993) Bayesian computation via the Gibbs sampler and related Markov chain Monte Carlo methods. J. R. Statist. Soc. B, 55, 3-23.
39. Vecchia, A. V. (1988) Estimation and model identification for continuous spatial processes. J. R. Statist. Soc. B, 50, 297-312.