Compound optimal spatial designs

A single purpose design may be quite inefficient for handling a real-life problem. Therefore, we often need to incorporate more than one design criterion and a common approach is simply to construct a weighted average, which may depend upon different information matrices. Designs based upon this method have been termed compound designs. The need to satisfy more than one design criterion is particularly relevant in the context of random fields. It is evident that for precise universal kriging it is important not only to efficiently estimate the spatial trend parameters, but also the parameters of the variogram or covariance function. Both tasks could for instance be comprised by applying corresponding design criteria and constructing a compound design from there. Modern techniques for such first and second order characteristics will be suggested and reviewed in the presentation. A new hybrid stochastic exchange type optimization algorithm is proposed and an illustrating example of the design of a water-quality monitoring network is provided. Copyright (C) 2009 John Wiley & Sons, Ltd.