Showing papers by "William G. Hunter published in 1968"

The Design of Experiments for Parameter Estimation

Abstract: This paper is concerned with the design of experiments to estimate the parameters in a model of known form, which may be nonlinear in the parameters. This problem was discussed in detail by Box and Lucas for the case where N, the number of experiments, is equal to p, the number of parameters. The present work is an extension to cases where N is greater than p. Conditions are established under which, when the number of experiments is a multiple of the number of parameters, replication of the best design for p experiments is an optimal design for N experiments. Several chemical examples are discussed; in each instance, the best design consists of simply repeating points of the original design for p experiments. An example is also mentioned where the best design does not consist of such replication.

A Joint Design Criterion for the Dual Problem of Model Discrimination and Parameter Estimation

Abstract: Two objectives of much experimentation in science and engineering are (i) to establish the form of an adequate mathematical model for the system being investigated and (ii) to obtain precise estimates of the model parameters. In the past, statistical design procedures have been proposed for tackling either one of these problems separately. Investigators, however, frequently want to perform experiments which will shed light on both questions simultaneously. In this paper, therefore, we present a design criterion which takes both objectives into account. The basic design strategy is to emphasize model discrimination when there is considerable doubt as to which model is best and gradually shifting the emphasis to parameter estimation as experimentation progresses and discrimination is accomplished. It is assumed that experiments can be performed sequentially. The use of the design criterion is illustrated with an example.