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ABSTRACT

In many applications, incorporating all the relevant information can be very difficult for various reasons. For instance, the data could be collected or constructed at different spatial scales, and the bias and measurement error of the available data might depend on the source of information.

We present a Bayesian methodology for spatial prediction with combined data. We model the observed data in terms of an underlying unobservable spatial process Z, and we obtain the posterior predictive values of Z given the available data from the different sources. In this work we take into account the lack of stationarity, spatial and temporal misalignment, potential bias and measurement error of the different sources of information.

We apply these methods to the prediction of air pollution concentrations by combining monitoring data with areal pollutant concentrations from the air quality numerical models run by EPA.