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HIERARCHIAL BAYESIAN CALIBRATION: AN APPLICATION TO AIRBORNE PARTICULATE MATTER MONITORING DATA
Citation:
McBride, S., M. Clyde, AND R W. Williams. HIERARCHIAL BAYESIAN CALIBRATION: AN APPLICATION TO AIRBORNE PARTICULATE MATTER MONITORING DATA. Presented at American Association for Aerosol Research, Boulder, CO, June 1-6, 2003.
Impact/Purpose:
The primary study objectives are:
1.To quantify personal exposures and indoor air concentrations for PM/gases for potentially sensitive individuals (cross sectional, inter- and intrapersonal).
2.To describe (magnitude and variability) the relationships between personal exposure, and indoor, outdoor and ambient air concentrations for PM/gases for different sensitive cohorts. These cohorts represent subjects of opportunity and relationships established will not be used to extrapolate to the general population.
3.To examine the inter- and intrapersonal variability in the relationship between personal exposures, and indoor, outdoor, and ambient air concentrations for PM/gases for sensitive individuals.
4.To identify and model the factors that contribute to the inter- and intrapersonal variability in the relationships between personal exposures and indoor, outdoor, and ambient air concentrations for PM/gases.
5.To determine the contribution of ambient concentrations to indoor air/personal exposures for PM/gases.
6.To examine the effects of air shed (location, season), population demographics, and residential setting (apartment vs stand-alone homes) on the relationship between personal exposure and indoor, outdoor, and ambient air concentrations for PM/gases.
Description:
In studies of the relationship between airborne fine particulate matter (PM2.5) and health, researchers frequently use monitoring data with the most extensive temporal coverage. Such data may come from a monitor that is not a federal reference monitor (FRM), a monitor that is designed and calibrated to meet federal National Ambient Air Quality Standards (NAAQS). In the recent past for the Phoenix area, measurements from a FRM have been available less frequently and have had levels of accuracy and bias that differed from a collocated equivalent (non-FRM) monitor. Using the soil constituent of PM2.5 as an illustration, we describe a Bayesian hierarchical model that combines information from collocated FRM and equivalent monitors to produce a temporally resolved posterior estimate of the complete concentration time series. Mean concentrations were modeled using a regression structure that reflected the influence of meteorology. To account for bias in monitors relative to each other, the mean at the equivalent monitor was represented by the product of an unknown bias parameter times the unknown mean concentration at the FRM monitor. Estimation of the bias parameter involved inference about the ratio of normal means as in the well-known Fieller-Creasy problem. We developed a multi-parameter, non-informative "reference prior" (Bernardo, 1979) for the hierarchical model that permitted simultaneous inference about the underlying mean concentrations and the bias parameter. By using a Bayesian calibration approach, the posterior distribution of unknown pollutant concentrations conditional on the measured data and model parameters could be estimated at all time points including those having missing data. Results characterized mean posterior concentrations and 95% credible intervals at the FRM and equivalent monitors, with the equivalent monitor showing larger concentrations than the FRM prior to an inlet upgrade and smaller concentrations after the inlet upgrade. The use of differing variances for each measurement within and between monitors ensured that large observations at either monitor did not have an undue influence on estimated posterior mean concentrations. For this case study, we describe the implications of using monitoring data from the biased equivalent monitor in models relating PM2.5 and health. Combining monitoring data from multiple monitors is of particular relevance to exposure-epidemiology panel studies, where multiple monitors have often been co-located and may have had missing data. Through hierarchical models that combine information from co-located monitors, we show that uncertainty in concentration measurements can be built into models of human exposure and health.
This work has been partially funded by the U.S. Environmental Protection Agency's Office of Research and Development under contracts 3D-5925-WATX (Sandra McBride), 68D-99-012 (RTI International), and cooperative agreement CR-828186-01-0 (Shaw University). It has been subjected to Agency review and approved for publication.