Bayesian areal interpolation, estimation, and smoothing: an inferential approach for geographic information systems. - Mugglin, A. S.; Carlin, B. P.; Zhu, L. (Environment & Planning A, 1999)
The writers outline a Bayesian approach to dealing with the fact that geographic information systems (GISs) typically feature little ability for statistical inference. The approach they present simultaneously permits Bayesian areal interpolation of missing values, estimation of the effect of relevant covariates, and spatial smoothing of underlying causal patterns. Their approach is implemented using Markov-chain Monte Carlo computational methods, and it automatically produces both point and interval estimates that explain all sources of uncertainty in the data. The writers describe the approach in the context of a simple, idealized example, and they demonstrate it with a data set on leukemia rates and potential geographic risk factors in Tompkins County, New York. Finally, they summarize their findings with numerous maps generated by using the popular GIS Arc/INFO.