Fully Model Based Approaches for Spatially Misaligned Data

In this paper we consider inference using multivariate data that are spatially misaligned i e involving variables typically counts or rates which are aggregated over di ering sets of regional boundaries Geographic information systems GISs enable the simultaneous display of such data sets but their current capabilities are essentially only descriptive not inferential We describe a hierarchical modeling approach which provides a natural solution to this problem through its abil ity to sensibly combine information from several sources of data and available prior information Illustrating in the context of counts allocation under non nested regional grids is handled us ing conditionally independent Poisson multinomial models Explanatory covariates and multilevel responses are also easily accommodated with spatial correlation modeled using a conditionally au toregressive CAR prior structure Methods for dealing with missing values in spatial edge zones are also discussed Like many recent hierarchical Bayesian applications computing is implemented via a carefully tailored Metropolis Hastings algorithm We illustrate our method with a complex data set involving inhalation exposure to radon emanating from a depleted uranium fuel processing plant in southwestern Ohio Structure counts obtained from U S Geological Survey topographical maps are used to realign sex and age group speci c U S Census block group population counts onto a cell circular windrose centered at the plant