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Bayesian wombling: finding rapid change in spatial maps

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In spatial analysis, typically we specify a region of interest and consider a spatial surface over the region. It is often of interest to ascertain where the surface is changing rapidly. Identifying locations or curves where there is rapid change is referred to as wombling. The surface may arise continuously over the region or discretely, in which case values are provided for a collection of areal units. In either setting, algorithmic strategies are available to attempt to identify so‐called wombling boundaries. In this study, the surfaces of interest are all assumed to be random, realizations of a Gaussian process in the continuous case, of a Markov random field in the discrete case. With specifications given as stochastic models, we discuss Bayesian approaches to implement desired boundary analysis. We refer to this as Bayesian wombling and show how fully model‐based inference can be carried out, including assessment of uncertainty. The approach for the continuous case is more theoretically demanding (expected with an uncountable set of locations) but yields elegant distribution theory. The discrete case is more straightforward. Each case is illustrated with a brief example. WIREs Comput Stat 2015, 7:307–315. doi: 10.1002/wics.1360 This article is categorized under: Statistical and Graphical Methods of Data Analysis > Bayesian Methods and Theory Data: Types and Structure > Image and Spatial Data Statistical and Graphical Methods of Data Analysis > Markov Chain Monte Carlo (MCMC)
Curvilinear boundary analysis on the spatial residual surface of temperature given precipitation, using GIS extracted boundary segments for the Colorado data.
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Lu and Carlin crisp (top 20%) wombled maps based on (a) SLDRs ηi and (b) residuals ϕi.
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Statistical and Graphical Methods of Data Analysis > Markov Chain Monte Carlo (MCMC)
Data: Types and Structure > Image and Spatial Data
Statistical and Graphical Methods of Data Analysis > Bayesian Methods and Theory

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