  DeGroot (1962) developed a general framework for constructing Bayesian
measures of the expected information that an experiment will provide for
estimation. We propose an analogous framework for measures of information for
hypothesis testing. In contrast to estimation information measures that are
typically used for surface estimation, test information measures are more
useful in experimental design for hypothesis testing and model selection. In
particular, we obtain a probability based measure, which has more appealing
properties than variance based measures in design contexts where decision
problems are of interest. The underlying intuition of our design proposals is
straightforward: to distinguish between models we should collect data from
regions of the covariate space for which the models differ most. Nicolae et al.
(2008) gave an asymptotic equivalence between their test information measures
and Fisher information. We extend this result to all test information measures
under our framework. Simulation studies and an application in astronomy
demonstrate the utility of our approach, and provide comparison to other
methods including that of Box and Hill (1967).
