Optimum experimental design for discriminating between two rival models in the presence of prior information

Abstract

SUMMARY The design of experiments for discriminating between two rival models in the presence of prior information is analyzed. The method of Atkinson & Fedorov is extended. A theorem derived from the Kiefer-Wolfowitz General Equivalence Theorem is used to construct and check optimal designs. Some examples are provided. This paper is concerned with the design of experiments for discriminating between two regression models, one or both of which may be nonlinear in the parameters. Atkinson & Fedorov (1975a) describe T-optimum designs for this purpose which are optimum when it is known which one of the models is true. The designs, which satisfy an equivalence theorem of optimum design theory, are locally optimum, in the sense that they depend upon the values of the unknown parameters of the true model. In the present paper we extend the theory to situations in which there is a specified prior probability that each model is true and, conditionally on this probability, prior distributions for the parameters in the two models are specified. Our central result is that such designs again satisfy an equivalence theorem which can be used both for the construction of designs and for checking the optimality of a proposed design. In the next section we give the background to the problem and introduce our notation. The equivalence theorem for T-optimum designs with prior distributions is presented in ? 3. Examples are in ? 4. 2. BACKGROUND The aim of the experiment is to maximize the expected noncentrality parameter of the false model, the expectation being taken over models and over the prior distributions of the parameters. To be more precise we introduce our notation which is based on that of Silvey (1980, Ch. 3). Let , a compact set, be the design region; let X be the class of all probability