Bayesian predictive inference for the proportion of eroded land in a small area in Iowa

There is an increasing interest in the quality of soil, especially for small geographical areas. We present a method to estimate the percent of the area in a county or hydrological basin that is eroded. There are sample data (for several counties in eastern Iowa) from the National Resources Inventory and population data on land use, land capability class, rainfall and slope length and steepness. Using the Gibbs sampler we perform Bayesian predictive inference to obtain estimates for the non-sampled units. These estimates, together with the sample data, provide an estimate of the proportion of the total area that is eroded. We assess the quality of fit of our model using two cross-validation exercises and graphical methods.