Page 186 - Modern Spatiotemporal Geostatistics

Modifications of BME Analysis 167

(c) Th e health damage indicator of a populatio n

where B(p k) is the density of receptors in the neighborhood of V(p k), and
X(p k) is a specified health effect (see "Human-exposure systems" on p. 182).
In the functional case of Equation 9.1, the basic equations of BME analysis
are easily modified as follows. The Lagrange multipliers ^ a are the solutions
of the system of moment equations

where XA 's a realization of the functional random field (Eq. 9.1); the
BMEmode equation is

and the posterior pdf is

where The form of the ^-operator in Equations 9.6 and
9.7 depends on the knowledge available. In the case of the knowledge described
in Proposition 6.1 (p. 126), the ^-operator has the form used in Equation 6.1
(p. 126); then, Equations 9.6 and 9.7 reduce to

and

The g a's are now functions of the point and the functional random fields
(e.g., they may include point and block covariances and point-block covariances
as well). The analysis can be generalized in terms of the operators shown in
Table 6.1 (p. 133) or any other posterior operator available.

EXAMPLE 9.1: The average ozone exposure XT = E during each day was
calculated from Equation 9.3 for a geographical region in the eastern U.S. that
includes New York City and Philadelphia. It was assumed that r e = 24 hr,
/ e = 100%, and X = E\-h is the 1-hr ozone exposure (in ppm). In Figure
9.1, the temporally averaged 1-hr ozone exposure maps are plotted for a few
selected days in July of 1995. These maps can help us detect variations in