Hierarchical Bayesian calibration with reference priors: An application to airborne particulate matter monitoring data

During an USEPA study in the Phoenix area from 1995-1998, measurements from a federal reference method (FRM) monitor, calibrated in accordance with National Ambient Air Quality Standards, were available less frequently with levels of accuracy and bias that differed from a colocated non-FRM or equivalent monitor. Using the soil constituent of PM2.5 (particles of aerodynamic particle diameter less than 2.5 micrometers (μm)) as an illustration, a Bayesian hierarchical calibration model is developed that combines information from reference and equivalent monitors to produce a temporally resolved posterior distribution of the complete concentration time series. Mean concentrations are modeled using a regression structure that reflects the influence of meteorology. To account for bias in monitors relative to each other, the mean at the equivalent monitor is represented by the product of an unknown bias parameter times the unknown mean concentration at the reference monitor. Estimation of the bias parameter involves inference about the ratio of normal means as in the well-known Fieller-Creasy problem. A new multi-parameter reference prior is developed for this comparative calibration setting, permitting simultaneous inference about the underlying mean concentrations and the bias parameter. By using a Bayesian hierarchical approach, the posterior distribution of unknown pollutant concentrations conditional