Bayesian Spatially Varying Regression Coefficients

Spatial smoothing techniques are often employed to estimate mean trends over some spatial and or time domain. An explosion of new estimation methods in the last 15 or so years have improved upon simple multiple regression and Kriging options often found in commercial GIS systems. Spatial regression models for a general linear model setting with different possible link functions and using CAR(conditional autoregressive) or SAR(spatial) error structures were among the early additions. Extensions to hierarchical models allow for additional model complexity at the cost of increased computational burden.The following Article by authors Wheeler and Walker illustrate how the use of Bayesian Spatially Varying Regression Coefficient models improved upon older methods such as Kriging in solving the estimation of the effects of barriers to the transmission of rabies. The estimation of their models were carried out in WinBugs software via MCMC sampling for Bayesian Spatially Varying Regression Coefficient models using MCAR(multivariate conditional autoregressive) errors. To see the inference impact of such models on a per covariate(spatial) basis, one set of maps in Figure 4., illustrates very nicely what is missing in simpler maps and models. This Article presents some statistical background.