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By Adrian E. Raftery (Editor), Martin A. Tanner (Editor), Martin T. Wells (Editor)

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Such a standard is not enforceable, because the expected number of exceedances is not directly measurable, and measurements cannot be taken everywhere in the region. Rather, it describes an ideal of compliance and may be termed an ideal standard. The standard is implemented by requiring that each site in an approved monitoring network have no more than three exceedances in 3 years. In effect, this © 2002 by American Statistical Association rule applies the law of large numbers to n = 3. Barnett and O’Hagan (1997) introduced the concept of statistically realizable ideal standards.

Here the chemical analysis determines the distribution of chemical species among the particles. Regression on known pollution profiles enables identification of sources (Park, Spiegelman, and Henry 1999), but the aforementioned compositional analysis approach may yield additional insight, particularly into seasonal patterns. 3. SPATIAL PREDICTION Environmental monitoring data are often used to develop regional summaries of pollution fields. To do so, values at unobserved sites have to be predicted.

L. , and de Jong, G. (1999), “MCMC Based Estimation of Variance Components in a Very Large Dairy Cattle Data Set,” Computational Cattle Breeding 99, Helsinki: MTT. Kempthorne, O. (1954), “The Correlation Between Relatives in a Random Mating Population,” Royal Society (London) Proceedings, Ser. B, 143, 103–113. Lindley, D. , and Smith, A. F. M. (1972), “Bayes Estimates for the Linear Model” (with discussion), Journal of the Royal Statistical Society, Ser. B, 34, 1–41. Lush, J. L. (1931), “The Number of Daughters Necessary to Prove a Sire,” Journal of Dairy Science, 14, 209–220.

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