Optimal Design for Correlated Processes

The project ist undertaken in collaboration with the Department of Applied Statistics of the University of Klagenfurt under the supervision of Professor J.Pilz. In many application fields the lack of optimal design methods in the presence of correlated observations has been felt for quite a time. Those fields contain computer simulation experiments, monitoring, contingent valuation studies and the whole area of environmental statistics. During the past 30 years a number of papers have been devoted to this particular subject and a variety of differing approaches have been proposed. Two very promising ones are firstly, to extend the definition of the information matrix of an experimental design by adding design dependent virtual noise to the considered regression model and secondly, to expand the covariance kernel to eventually allow for Bayesian techniques. Since these approaches are new, many of their properties and potential are yet to be explored, leaving a large area of work for a theoretic statistician. The named methods have particular importance in spatial problems, such as monitoring sensor location. The investigation of this aspect and a development of a unifying view of these design methods will be a major objective of this project. The two other goals of the study are the establishment of the methods of extending information matrices and eigenvector expansions as standard tools in optimal design theory, and the propagation and the use of these methods in application areas of spatial statistics (or areas where non-standard regression models such as correlated random fields are applied).

Our project was focused on problems that need research and development in many actual European research areas in order to be operational for all the applications it is designed for. These potential areas are genomics and biotechnology for health, information society technologies through the generation of knowledge-based systems for natural resource management and for risk prevention and crisis management including humanitarian mine clearance, aeronautics and space, food quality and safety, sustainable development, global change and ecosystems, citizens and governance in a knowledge-based society and nuclear energy. Within these application fields there are a number of problems, for which optimal design theory for correlated observations could be effectively applied. In the geological sciences for instance one could employ similar techniques for constructing earthquake monitoring networks. Another area of interest is the geochemical surveying of potentially contaminated land. In practice, only a limited number of samples are analyzed while soil is often a highly heterogeneous material. Consequently, the spatial variation of the geochemical properties is generally poorly quantified, possibly affecting the accuracy with which significantly contaminated areas are delineated. In recognition of this weakness, a popular strategy is to subdivide an area into distinct units using available historical information and/or easily identifiable characteristics. Subsequently, the sampling effort assigned to each unit is weighted proportionally to the expected local contamination. The primary purpose of the subsequent sampling campaign is to verify whether the assumed spatial distribution of the contamination was correct. While this strategy can potentially improve the accuracy of the assessment, cross-validation with statistical techniques remains essential. By the better development and propagation of the above described methods a more widespread application of optimal design techniques (and thus more precise experimental results) in many application fields must be expected. This would then lead to new theoretical problems arising and therefore to a mutual fertilization of the respective disciplines.