Estimation or simulation of soil properties? An optimization problem with conflicting criteria

Both estimation and simulation approaches are formulated as the selection of a set of attribute values that are optimal for criteria that are typically conflicting. Estimation amounts to minimize local criteria such as a local error variance, whereas stochastic simulation aims to reproduce global statistics such as the histogram or semivariogram. A simulated annealing (SA) algorithm is presented to generate maps of optimal values: an initial random image is gradually perturbed so as to minimize a weighted combination of three components that measure deviations from local or global features of interest. The approach is illustrated using an environmental data set related to soil contamination by zinc. A validation set shows that, depending on the relative weight given to local and global constraints, the final maps have properties ranging from estimation to simulation in terms of mean square error (MSE) of prediction and extent of the space of uncertainty. Combination of both types of constraints leads to better performances (smaller proportions of misclassified locations, smaller prediction errors for the average proportion of contaminated locations within remediation units) than a smooth estimated map or a simulated map that reproduces only the histogram and semivariogram.