A class of covariate-dependent spatiotemporal covariance functions for the analysis of daily ozone concentration

Annals of Applied Statistics

Volumn 5, Issue 4, 2011, Pages 2425-2447

  Reich, Brian J ^a   Eidsvik, Jo ^a   Guindani, Michele ^a   Nail, Amy J ^a   Schmidt, Alexandra M ^a  

^a NONE

Author keywords

Covariance estimation; Nonstationarity; Ozone; Spatial data analysis

Indexed keywords

EID: 84868610548     PISSN: 19326157     EISSN: 19417330     Source Type: Journal    
DOI: 10.1214/11-AOAS482     Document Type: Article

References (36)

1. Adler, R. J. (1981). The Geometry of Random Fields. Wiley, London.
2. Banerjee, S. and Gelfand, A. E. (2003). On smoothness properties of spatial processes. J. Multivariate Anal. 84 85-100.
3. Banerjee, S., Gelfand, A. E. and Sirmans, C. F. (2003). Directional rates of change under spatial process models. J. Amer. Statist. Assoc. 98 946-954.
4. Berrocal, V. J., Gelfand, A. E. and Holland, D. M. (2010). A spatio-temporal downscaler for output from numerical models. J. Agric. Biol. Environ. Stat. 15 176-197.
5. Carroll, R., Chen, R., George, E., Li, T., Newton, H., Schmiediche, H. and Wang, N. (1997). Ozone exposure and population density in Harris County, Texas. J. Amer. Statist. Assoc. 92 392-404.
6. CFR (2008). 40 CFR Parts 50 and 58, National Ambient Air Quality Standards for Ozone, Final rule.
7. Cooley, D., Nychka, D. and Naveau, P. (2007). Bayesian spatial modeling of extreme precipitation return levels. J. Amer. Statist. Assoc. 102 824-840.
8. Cressie, N. and Huang, H.-C. (1999). Classes of nonseparable, spatio-temporal stationary covariance functions. J. Amer. Statist. Assoc. 94 1330-1340.
9. Dou, Y., Le, N. D. and Zidek, J. V. (2010). Modeling hourly ozone concentration fields. Ann. Appl. Stat. 4 1183-1213.
10. Fuentes, M. (2002). Spectral methods for nonstationary spatial processes. Biometrika 89 197-210.
11. Gelfand, A. E., Kim, H.-J., Sirmans, C. F. and Banerjee, S. (2003). Spatial modeling with spatially varying coefficient processes. J. Amer. Statist. Assoc. 98 387-396.
12. Gilleland, E. and Nychka, D. (2005). Statistical models for monitoring and regulating ground-level ozone. Environmetrics 16 535-546.
13. Gneiting, T. (2002). Nonseparable, stationary covariance functions for space-time data. J. Amer. Statist. Assoc. 97 590-600.
14. Guttorp, P., Meiring, W. and Sampson, P. D. (1994). A space-time analysis of ground-level ozone data. Environmetrics 5 241-254.
15. Higdon, D., Swall, J. and Kern, J. (1999). Non-stationary spatial modeling. In Bayesian Statistics 6-Proceedings of the Sixth Valencia Meeting (J. M. Bernardo, J. O. Berger, A. P. Dawid and A. F. M. Smith, eds.) 761-768. Clarendon, Oxford.
16. Huang, H. C. and Hsu, N. J. (2004). Modeling transport effects on ground-level ozone using a non-stationary space-time model. Environmetrics 15 251-268.
17. Huerta, G., Sansó, B. and Stroud, J. R. (2004). A spatiotemporal model for Mexico City ozone levels. J. R. Stat. Soc. Ser. C. Appl. Stat. 53 231-248.
18. Kent, J. T. (1989). Continuity properties for random fields. Ann. Probab. 17 1432-1440.
19. Li, Y., Tang, H. and Lin, X. (2009). Spatial linear mixed models with covariate measurement errors. Statist. Sinica 19 1077-1093.
20. Lopes, H. F., Gamerman, D. and Salazar, E. (2011). Generalized spatial dynamic factor models. Comput. Statist. Data Anal. 55 1319-1330.
21. Lopes, H. F., Salazar, E. and Gamerman, D. (2008). Spatial dynamic factor analysis. Bayesian Anal. 3 759-792.
22. McMillan, N., Bortnick, S. M., Irwin, M. E. and Berliner, L. M. (2005). A hierarchical Bayesian model to estimate and forecast ozone through space and time. Atmospheric Environment 39 1373-1382.
23. Meiring, W., Guttorp, P. and Sampson, P. D. (1998). Space-time estimation of grid-cell hourly ozone levels for assessment of a deterministic model. Environ. Ecol. Stat. 5 197-222.
24. Nail, A. J., Hughes-Oliver, J. M. and Monahan, J. F. (2010). Quantifying local creation and regional transport using a hierarchical space-time model of ozone as a function of observed NOx, a latent space-time VOC process, emissions, and meteorology. J. Agric. Biol. Environ. Stat. 16 17-44.
25. Paciorek, C. J. (2010). The importance of scale for spatial-confounding bias and precision of spatial regression estimators. Statist. Sci. 25 107-125.
26. Paciorek, C. J. and Schervish, M. J. (2006). Spatial modelling using a new class of nonstationary covariance functions. Environmetrics 17 483-506.
27. Paciorek, C. J., Yanosky, J. D., Puett, R. C., Laden, F. and Suh, H. H. (2009). Practical large-scale spatio-temporal modeling of particulate matter concentrations. Ann. Appl. Statist. 3 370-397.
28. Reich, B. J., Hodges, J. S. and Zadnik, V. (2006). Effects of residual smoothing on the posterior of the fixed effects in disease-mapping models. Biometrics 62 1197-1206.
29. Sahu, S. K., Gelfand, A. E. and Holland, D. M. (2007). High-resolution space-time ozone modeling for assessing trends. J. Amer. Statist. Assoc. 102 1221-1234.
30. Sampson, P. D. and Guttorp, P. (1992). Nonparametric estimation of nonstationary covariance structure. J. Amer. Statist. Assoc. 87 108-119.
31. Schmidt, A. M., Guttorp, P. and O'Hagan, A. (2011). Considering covariates in the covariance structure of spatial processes. Environmetrics 22 487-500.
32. Schmidt, A. M. and O'Hagan, A. (2003). Bayesian inference for nonstationary spatial covariance structures via spatial deformations. J. R. Stat. Soc. Ser. B Stat. Methodol. 65 743-775.
33. Schmidt, A. M. and Rodríguez, M. A. (2011). Modelling multivariate counts varying continuously in space. In Bayesian Statistics 9-Proceedings of the Sixth Valencia Meeting (J. M. Bernardo, M. J. Bayarri, J. O. Berger, A. P. Dawid, D. Heckerman, A. F. M. Smith and M. West, eds.). Clarendon, Oxford.
34. Stein, M. L. (2005). Space-time covariance functions. J. Amer. Statist. Assoc. 100 310-321.
35. Stein, M. L. and Fang, D. (1997). Discussion of "Ozone exposure and population density in Harris County, Texas", by R. J. Carroll, et al. J. Amer. Statist. Assoc. 92 408-411.
36. Wakefield, J. (2007). Disease mapping and spatial regression with count data. Biostatistics 8 158-183.