Approximately optimal spatial design approaches for environmental health data

Environmetrics

Volumn 17, Issue 4, 2006, Pages 363-385

  Xia, Gangqiang ^a   Miranda, Marie Lynn ^a   Gelfand, Alan E ^a  

^a DUKE UNIVERSITY   (United States)

Author keywords

Block sampling; Entropy; Fisher information; Gaussian process; Sequential sampling; Stochastic search

Indexed keywords

ECOTOXICOLOGY; SPATIAL ANALYSIS; TOXICOLOGICAL PHENOMENA;

EID: 33745159356     PISSN: 11804009     EISSN: 1099095X     Source Type: Journal    
DOI: 10.1002/env.775     Document Type: Article

References (39)

1. Arbia G, Lafratta G. 2002. Anisotropic spatial sampling designs for urban pollution. Applied Statistics 51: 223-234.
2. Assunção RM. 2003. Space varying coefficients models for small area data. Environmetrics 14: 453-473.
3. Banerjee S, Carlin BP, Gelfand AE. 2004. Hierarchical Modeling and Analysis for Spatial Data. Chapman & Hall, CRC: London.
4. Bernardinelli L, Montomoli C. 1992. Empirical Bayes versus fully Bayesian analysis of geographical variation in disease risk. Statistics in Medicine 11: 983-1007.
5. Bogaert P, Russo D. 1999. Optimal spatial sampling design for the estimation of the variogram based on a least-squares approach. Water Resources Research 35: 1275-1289.
6. Brimkulov U, Krug G, Savanov V. 1986. Design of Experiments for Random Fields. Nauka: Moscow.
7. Brown PJ, Le ND, Zidek JV. 1994. Multivariate spatial interpolation and exposure to air pollutants. Canadian Journal of Statistics 22: 489-509.
8. Clayton DG, Kaldor JM. 1987. Empirical Bayes estimates of age-standardized relative risks for use in disease mapping. Biometrics 43: 671-681.
9. Cox DR, Hinkley DV. 1974. Theoretical Statistics. Chapman-Hall: London.
10. Cox DR, Reid N. 1987. Parameter orthogonality and approximate conditional inference (with discussion). Journal of the Royal Statistical Society B 49: 1-39.
11. Diggle PJ, Tawn JA, Moyeed RA. 1998. Model-based geostatistics (with discussion). Journal of Royal Statistical Society C 52: 299-350.
12. Dolinoy DC, Miranda ML. 2004. GIS modeling of air toxics releases from TRI-reporting and non-TRI-reporting facilities: impacts for environmental justice. Environmental Health Perspectives 112(17): 1717-1724.
13. Fedorov VV. 1996. Design of Spatial Experiments, Model Fitting and Prediction. Oak Ridge National Laboratory.
14. Gelfand AE, Banerjee S, Gamerman D. 2005. Spatial process modelling for univariate and multivariate dynamic spatial data. Environmetrics 16: 1-15.
15. Guttorp P, Meiring W, Sampson P. 1994. A space-time analysis of ground-level ozone data. Environmetrics 5: 241-254.
16. Harville DA. 1997. Matrix Algebra for a Statistician's Perspective. Springer: New York.
17. Huerta G, Sanso B, Stroud JR. 2004. A spatio-temporal model for Mexico City ozone levels. Applied Statistics 53: 231-248.
18. Knorr-Held L. 2002. Some remarks on Gaussian Markov random field models for disease mapping. In Highly Structured Stochastic Systems, Green PJ, Hjort NL, Richardson S (eds). Oxford University Press: Oxford.
19. Le N, Zidek JV. 1992. Interpolation with uncertain spatial covariances: a Bayesian alternative to kriging. Journal of Multivariate Analysis 43: 351-374.
20. McBratney AB, Webster R, Burgess TM. 1981. The design of optimal sampling schemes for local estimation and mapping of ragionalized variables. I. Theory and method. Computer & Geosciences 7(4): 331-334.
21. Miranda ML, Dolinoy D, Overstreet MA. 2002. Mapping for prevention: GIS models for directing childhood lead poisoning prevention programs. Environmental Health Perspectives 110(9): 947-953.
22. Müller WG. 2001. Collecting Data: Optimum Design of Experiments for Random Fields. Springer: New York.
23. Müller WG, Zimmerman DL. 1999. Optimal designs for variogram estimation. Environmetrics 10: 23-37.
24. Nychka D, Saltzman N. 1998. Design of air-quality monitoring networks. In Case Studies in Environmental Statistics, Lecture Notes in Statistics, Nychka D, Cox L, Piegorsch W (eds). Springer Verlag: New York.
25. Pukelsheim F. 1993. Optimum Design of Experiments. Wiley: New York.
26. Rao CR. 1973. Linear Statistical Inference and its Applications. Wiley: New York.
27. Ritter K. 1996. Asymptotic optimality of regular sequence designs. Annals of Statistics 24: 2081-2096.
28. Sacks J, Ylvisaker D. 1996. Design for regression problems with correlated errors. Annals of Statistics 37: 66-89.
29. Sahu S, Gelfand AE, Holland DM. 2005. Spatio-temporal modeling of fine particulant matter. Journal of Agricultural, Biological, and Environmental Statistics. (in press)
30. Schmidt AM, Gelfand AE. 2003. A Bayesian coregionalization approach to multivariate pollutant data. Journal of Geophysical Research - Atmosphere 108(D24): 8783.
31. Su Y, Cambanis S. 1993. Sampling design for estimation of a random process. Stochastic Process Applications 46: 47-89.
32. Shaddick G, Wakefiled J. 2002. Modelling multivariate pollutant data at multiple sites. Applied Statistics 51: 351-372.
33. Stein ML. 1999. Statistical Interpolation of Spatial Data: Some Theory for Kriging. Springer: New York.
34. Warrick AW, Myers DE. 1987. Optimization of sampling locations for variogram calculations. Water Resources Research 23: 496-500.
35. Xia G, Hjort NL, Gelfand AE. 2005. Information growth and consistent parameter estimation under stochastic process models with regression structure. Technical Report, ISDS, Duke University.
36. Zhu L, Carlin BP, Gelfand AE. 2003. Hierarchical regression with misaligned spatiotemporal data: relating ambient ozone and pediatric asthma visits in Atlanta. Environmetrics 14: 537-557.
37. Zhu Z. 2002. Optimal sampling design and parameter estimation of Gaussian random fields. PhD Thesis. Department of Statistics, University of Chicago.
38. Zhu Z, Stein M. 2005. Spatial sampling design for parameter estimation of the covariance function. Journal of statistical planning and inference. (in press)
39. Zidek JV, Sun W, Le ND. 2000. Designing and integrating composite networks for monitoring multivariate Gaussian pollution fields. Applied Statistics and Computing 49: 63-79.