Mining boundary effects in areally referenced spatial data using the Bayesian information criterion

Pei Li, Sudipto Banerjee, Alexander M McBean

Research output: Contribution to journalArticlepeer-review

18 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)435-454
Number of pages20
Issue number3
StatePublished - Jul 2011

Bibliographical note

Funding Information:
This work was supported in part by NIH grants 1-R01-CA95995 and 1-RC1-GM092400-01.


  • Areal data
  • Bayesian information criteria
  • Boundaries
  • Conditionally autoregressive models
  • Simultaneous autoregressive models
  • Wombling


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