Bayesian wombling: Finding rapid change in spatial maps

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.

Duke Scholars

Author Alan E. Gelfand Statistical Science