Modeling hourly ozone concentration fields. (English) Zbl 1202.62169

Summary: This paper compares two methods built on a hierarchical Bayesian foundation and designed for modeling hourly ozone concentrations over the eastern United States. One, a dynamic linear state space model (DLM), that has been proposed earlier [G. Huerta et al., J. R. Stat. Soc., Ser. C 53, No. 2, 231–248 (2004; Zbl 1111.62372)], lies in a very contemporary setting where two historical paths to temporal process models, the Kalman filter and the dynamic system with random perturbations, converge. The other, which we call the Bayesian spatial predictor (BSP), is a Bayesian alternative to the purely spatial method of kriging. The DLM as a dynamic system model has parameters that are states of the process which generate the ozone and change with time. More specifically, the model includes a time-varying site invariant mean field as well as time-varying coefficients for 24 and 12 hour diurnal cyclic components. The resulting model’s great flexibility comes at the cost of complexity, forcing the use of an MCMC approach and very time-consuming computations. Thus, the size of the DLM’s spatial domain of applicability has to be restricted and the number of monitoring sites that can be treated limited. The paper’s assessment of the DLM reveals other difficulties that point to the need to consider a less flexible competitor, a Bayesian spatial predictor (BSP). The two methods are compared in a variety of ways and overall conclusions given. In particular, the conclusions point to the BSP as the more practical alternative for spatial prediction.


62P12 Applications of statistics to environmental and related topics
62F15 Bayesian inference
62M30 Inference from spatial processes


Zbl 1111.62372


R; EnviroStat
Full Text: DOI arXiv


[1] Burke, J. M., Zufall, M. J. and Özkaynak, H. (2001). A population exposure model for particulate matter: Case study results for PM 2.5 in Philadelphia, PA. J. Expo. Anal. Env. Epid. 11 470-489.
[2] Calder, C. A., Holloman, C. H., Bortnick, S. M., Strauss, W. J. and Morara, M. (2008). Relating ambient particulate matter concentration levels to mortality using an exposure simulator. J. Amer. Statist. Assoc. 103 137-148. · Zbl 1469.62388 · doi:10.1198/016214507000000392
[3] Carter, C. K. and Kohn, R. (1994). On Gibbs sampling for state space models. Biometrika 81 541-553. · Zbl 0809.62087 · doi:10.1093/biomet/81.3.541
[4] Dou, Y. P., Le, N. D. and Zidek, J. V. (2007). A dynamic linear model for hourly ozone concentrations. Technical Report 228, Dept. Statistics, Univ. British Columbia. Available at .
[5] Dou, Y. P., Le, N. D. and Zidek, J. V. (2009a). Temporal prediction with a Bayesian spatial predictor: An application to ozone fields. Technical Report 249, Dept. Statistics, Univ. British Columbia. Available at .
[6] Dou, Y. P., Le, N. D. and Zidek, J. V. (2009b). Supplement to “Modeling hourly ozone concentration fields.” DOI: . · Zbl 1202.62169
[7] Dou, Y. P., Le, N. D. and Zidek, J. V. (2009c). Supplement to “Modeling hourly ozone concentration fields.” DOI: . · Zbl 1202.62169
[8] Huerta, G., Sansó, B. and Stroud, J. R. (2004). A spatio-temporal model for Mexico city ozone levels. J. Roy. Statist. Soc. Ser. C-App. 53 231-248. · Zbl 1111.62372 · doi:10.1046/j.1467-9876.2003.05100.x
[9] Le, N. D. and Zidek, J. V. (1992). Interpolation with uncertain spatial covariances: A Bayesian alternative to Kriging. J. Multivariate Anal. 43 351-374. · Zbl 0762.62025 · doi:10.1016/0047-259X(92)90040-M
[10] Le, N. D. and Zidek, J. V. (2006). Statistical Analysis of Environmental Space-Time Processes . Springer, New York. · Zbl 1102.62126
[11] Lemos, R. T., Sansó, B. and Los Huertos, M. (2007). Spatially varying temperature trends in a central California estuary. J. Agric. Biol. Environ. Stat. 12 379-396. · Zbl 1306.62306 · doi:10.1198/108571107X227603
[12] Li, K. H., Le, N. D., Sun, L. and Zidek, J. V. (1999). Spatial-temporal models for ambient hourly PM 10 in Vancouver. Environmetrics 10 321-338.
[13] Ozone (2006). Air quality criteria for ozone and related photochemical oxidants. National Center for Environmental Assessment. RTP: US Environmental Protection Agency. Available at .
[14] Shaddick, G., Lee, D., Zidek, J. V. and Salway, R. (2008). Estimating exposure response functions using ambient pollution concentrations. Ann. Appl. Statist. 2 1249-1270. · Zbl 1168.62397 · doi:10.1214/08-AOAS177
[15] Stroud, J. R., Muller, P. and Sansó, B. (2001). Dynamic models for spatio-temporal data. J. Roy. Statist. Soc. Ser. B 63 673-689. · Zbl 0986.62074 · doi:10.1111/1467-9868.00305
[16] West, M. and Harrison, J. (1997). Bayesian Forcasting and Dynamic Models , 2nd ed. Springer, New York. · Zbl 0871.62026
[17] Zidek, J. V., Sun, L., Le, N. D. and Özkaynak, H. (2002). Contending with space-time interaction in the spatial prediction of pollution: Vancouver’s hourly ambient PM 10 field. Environmetrics 13 595-613.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.