Optimal designs for spatio-temporal data

A01 has its focus on optimal design of experiments to increase the accuracy of spatio-temporal data analysis. It will develop a novel approach by considering the estimation and design problem simultaneously in continuous spatio-temporal models followed by the construction of implementable designs and estimators by appropriate discrete approximations. The long-term goal is the development of a unifying optimal design methodology for spatio-temporal modeling including models based on partial and stochastic partial differential equations.

We determine optimal designs of experiments to increase the accuracy of statistical analysis of spatio-temporal data following a model-based approach. The main focus is on the development of a general methodology using the transition between discrete and continuous data structures. In particular, we determine the likelihood function, Fisherinformation matrix, maximum likelihood estimators and designs for models that are discrete in space and continuous in time, and use these results to derive efficient and implementable designs by discrete approximations of the optimal (continuous) solutions.

As it is often difficult to specify a concrete model in the stage of designing experiments, a large part of the project is devoted to the problem of constructing efficient designs under model uncertainty. Here we concentrate on designs that are robust with respect to model assumptions (using compound, Bayesian and minimax criteria that take the model uncertainty into account) and on designs for model validation developing new concepts of optimal discrimination designs for the analysis of spatio-temporal data (such as optimality criteria based on the Kullback-Leibler distance). Moreover, we also construct optimal designs for model-averaging estimates and determine efficient designs for state space models for networks and for spatial functional models.

An important aspect that will be addressed throughout this project, is scalability, as optimization has to be performed over large dimensional spaces often. Typical challenges include the calculation of optimal discrete approximations, of Bayesian and minimax optimal (discrimination) designs and of optimal designs for state space models.