Bayesian Areal Wombling for Geographical Boundary

• Activity Number: 74
• Type: Contributed
• Date/Time: Sunday, August 7, 2005 : 8:00 PM to 9:50 PM
• Sponsor: ENAR
• Author(s): Bradley P. Carlin and Haolan Lu*+
• Companies: University of Minnesota and University of Minnesota
• Keywords: Areal data ; Conditionally autoregressive model ; Hierarchical Bayesian model ; Markov chain Monte Carlo simulation ; spatial statistics

Abstract

In the analysis of spatially referenced data, interest often focuses not on prediction of the spatially indexed variable, but on boundary analysis. Existing boundary analysis methods are sometimes generically referred to as wombling (Womble 1951). When data are available at point level, such boundaries are most naturally obtained by locating the points of steepest ascent or descent on the fitted spatial surface (Banerjee et al. 2004). In this paper, we propose related methods for areal data. Such methods are valuable in determining boundaries for datasets available only in ecological format. After a brief review of existing algorithmic techniques, we propose a fully model-based framework for areal wombling, using Bayesian hierarchical models with posterior summaries computed using Markov chain Monte Carlo methods. We explore the suitability of various existing hierarchical and spatial software packages to the task and show the approach's superiority over existing nonstochastic alternatives, both in terms of utility and average mean square error behavior. We also illustrate our methods using Minnesota colorectal cancer late detection data.