JSM 2004 - Toronto

Abstract #300016

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Activity Number: 366
Type: Invited
Date/Time: Wednesday, August 11, 2004 : 2:00 PM to 3:50 PM
Sponsor: ENAR
Abstract - #300016
Title: Bayesian Wombling for Areal Data
Author(s): Brad Carlin*+ and Haolan Lu
Companies: University of Minnesota and University of Minnesota
Address: MMC 303, Division of Biostatistics, Minneapolis, MN, 55455,
Keywords: posterior distribution ; MCMC ; spatial data
Abstract:

Boundary analysis is the name given by geographers to the use of spatially oriented data to determine boundaries separating areas of dissimilar values on a map. "Wombling" is the name of an algorithmic approach (due to Womble, 1951) which uses spatial gradients computed from point level data, after which regional boundaries are constructed "from scratch." With areal (say, zip or county) level data, however, boundary analysis methods must use a subset of the existing set of (typically geopolitical) boundaries. We offer a Bayesian solution to this problem, which allows full inference regarding the existence of a boundary separating any two regions. The analogues of "crisp" and "fuzzy" wombling arise naturally by determining the boundaries using either the posterior means of the metrics themselves, or the posterior probabilities that they exceed a given level, respectively. The Bayesian framework also enables easy inference regarding the uncertainty of any boundary or group of boundaries (the latter via multivariate summaries). We illustrate our approach using a dataset on late detection of colorectal and breast cancer in Minnesota counties.

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