This paper investigates the effect of prior information on the design of experiments for detecting the potential impact of an event which is to occur at a specified time, in the knowledge of possible overall changes to the population as a whole. It is assumed that an F test of interaction is to be used to decide if an impact has occurred. Maximizing the power of this test, or rather the simpler, closely related goal of maximizing the noncentrality parameter is taken to be the designer's objective. Some of the results obtained are qualitative. For example, for certain fairly realistic general models of how a subregional impact might distribute itself, it is shown that it is never optimal to place more than 50% of the monitoring sites in any one of the homogeneous subregions in which the impact might occur. Another qualitative, more intuitively obvious result is that it is essential to monitor subregions where the impact is not likely to occur ("quasicontrols"); this would maximize the contrast created by the potential impact. A very general solution to the optimal design problem is given in a form which could be readily implemented in practice with the aid of a computer. Explicit solutions are also given for certain realistic impact models.
"Using Prior Information in Designing Intervention Detection Experiments." Ann. Statist. 21 (1) 447 - 463, March, 1993. https://doi.org/10.1214/aos/1176349036