Experimental Design for Time-Dependent Models with Correlated Observations

Abstract

We describe an algorithm for the construction of optimum experimental designs for the parameters in a regression model when the errors have a correlation structure. Our example is drawn from chemical kinetics, so that the model is nonlinear. Our algorithm has been implemented to be used when the model consists of a set of differential equations for which only numerical solutions ar available. However, the algorithm can also be used for standard regression models when the errors are correlated. The paper concludes with some discussion of outstanding issues in optimum design with correlated errors.

Modeling the Dynamics of the Cardiovascular-respiratory System (CVRS) in Humans, a Survey

“…The assumption that the E(t N j ) are independent may be not satisfied, for instance, in cases where the sampling times are close to each other. In such a case one has to consider correlated measurements (see [91]). …”

Sensor network design for the estimation of spatially distributed processes

“…In the context of parameter estimation, exceptions to this naive approach constitute the works originating in statistical optimum experimental design (Fedorov and Hackl, 1997;Walter and Pronzato, 1997;Uciński and Bogacka, 2005;Uciński and Atkinson, 2004), and its extensions to models for dynamic systems, especially in the context of the optimal choice of sampling instants and input signals (Ljung, 1999;Gevers, 2005;Hjalmarsson, 2005). In this vein, various computational schemes have been developed to directly attack the original problem or its convenient approximation.…”

A comparison of spatial design methods for correlated observations

“…However, the above given statistical interpretation makes clear why an improvement of the design by a correction algorithm based upon (6) can be expected. Unfortunately there exists no proof of convergence of this heuristic algorithm (as in the uncorrelated case) and, although refinements of the procedure have been suggested (see, for example, Section 6.6 of Näther, 1985, and for a recent implementation Ucinski and Atkinson, 2004), none of them apparently guarantees perfect performance. Indeed there are many instances where in simulation experiments severe failures of finding the optimum have been reported (see Glatzer and Müller, 1999).…”