We characterize those coherent design criteria which depend only on the dispersion matrix (assumed proper and nonsingular) of the “state of nature,” which may be a parameter-vector or a set of future observables, and describe the associated decision problems. Connections are established with the classical approach to optimal design theory for the normal linear model, based on concave functions of the information matrix. Implications of the theory for more general models are also considered.
"Coherent dispersion criteria for optimal experimental design." Ann. Statist. 27 (1) 65 - 81, February 1999. https://doi.org/10.1214/aos/1018031101