Bayesian areal wombling via adjacency modeling |
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Authors: | Haolan Lu Cavan S Reilly Sudipto Banerjee Bradley P Carlin |
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Institution: | (1) Bristol-Myers Squibb Company, 5 Research Parkway, Wallingford, CT 06492, USA;(2) Division of Biostatistics, School of Public Health, University of Minnesota, Mayo Mail Code 303, Minneapolis, MN 55455, USA |
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Abstract: | Recently, public health professionals and other geostatistical researchers have shown increasing interest in boundary analysis, the detection or testing of zones or boundaries that reveal sharp changes in the values of spatially oriented variables.
For areal data (i.e., data which consist only of sums or averages over geopolitical regions), Lu and Carlin (Geogr Anal 37: 265–285,
2005) suggested a fully model-based framework for areal wombling using Bayesian hierarchical models with posterior summaries
computed using Markov chain Monte Carlo (MCMC) methods, and showed the approach to have advantages over existing non-stochastic
alternatives. In this paper, we develop Bayesian areal boundary analysis methods that estimate the spatial neighborhood structure
using the value of the process in each region and other variables that indicate how similar two regions are. Boundaries may then be determined by the posterior distribution
of either this estimated neighborhood structure or the regional mean response differences themselves. Our methods do require
several assumptions (including an appropriate prior distribution, a normal spatial random effect distribution, and a Bernoulli
distribution for a set of spatial weights), but also deliver more in terms of full posterior inference for the boundary segments
(e.g., direct probability statements regarding the probability that a particular border segment is part of the boundary).
We illustrate three different remedies for the computing difficulties encountered in implementing our method. We use simulation
to compare among existing purely algorithmic approaches, the Lu and Carlin (2005) method, and our new adjacency modeling methods.
We also illustrate more practical modeling issues (e.g., covariate selection) in the context of a breast cancer late detection
data set collected at the county level in the state of Minnesota. |
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Keywords: | Adjacency modeling Areal data Conditionally autoregressive (CAR) model Hierarchical Bayesian model Markov chain Monte Carlo (MCMC) simulation Spatial statistics |
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