Mining boundary effects in areally referenced spatial data using the Bayesian information criterion |
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Authors: | Pei Li Sudipto Banerjee Alexander M McBean |
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Affiliation: | (1) Division of Biostatistics, School of Public Health, University of Minnesota, Mayo Mail Code 303, Minneapolis, MN 55455–0392, USA;(2) Division of Health Policy & Management, School of Public Health, University of Minnesota, Minneapolis, MN 55455, USA |
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Abstract: | Statistical models for areal data are primarily used for smoothing maps revealing spatial trends. Subsequent interest often
resides in the formal identification of ‘boundaries’ on the map. Here boundaries refer to ‘difference boundaries’, representing
significant differences between adjacent regions. Recently, Lu and Carlin (Geogr Anal 37:265–285, 2005) discussed a Bayesian framework to carry out edge detection employing a spatial hierarchical model that is estimated using
Markov chain Monte Carlo (MCMC) methods. Here we offer an alternative that avoids MCMC and is easier to implement. Our approach
resembles a model comparison problem where the models correspond to different underlying edge configurations across which
we wish to smooth (or not). We incorporate these edge configurations in spatially autoregressive models and demonstrate how
the Bayesian Information Criteria (BIC) can be used to detect difference boundaries in the map. We illustrate our methods
with a Minnesota Pneumonia and Influenza Hospitalization dataset to elicit boundaries detected from the different models. |
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