Experimentation is at the core of research in the behavioral and neural sciences, yet observations can be expensive and time-consuming to acquire (e.g., MRI scans, responses from infant participants). A major interest of researchers is designing experiments that lead to maximal accumulation of information about the phenomenon under study with the fewest possible number of observations. In addressing this challenge, statisticians have developed adaptive design optimization methods. This letter introduces a hierarchical Bayes extension of adaptive design optimization that provides a judicious way to exploit two complementary schemes of inference (with past and future data) to achieve even greater accuracy and efficiency in information gain. We demonstrate the method in a simulation experiment in the field of visual perception.

Discriminating among competing statistical models is a pressing issue for many experimentalists in the field of cognitive science. Resolving this issue begins with designing maximally informative experiments. To this end, the problem to be solved in adaptive design optimization is identifying experimental designs under which one can infer the underlying model in the fewest possible steps. When the models under consideration are nonlinear, as is often the case in cognitive science, this problem can be impossible to solve analytically without simplifying assumptions. However, as we show in this letter, a full solution can be found numerically with the help of a Bayesian computational trick derived from the statistics literature, which recasts the problem as a probability density simulation in which the optimal design is the mode of the density. We use a utility function based on mutual information and give three intuitive interpretations of the utility function in terms of Bayesian posterior estimates. As a proof of concept, we offer a simple example application to an experiment on memory retention.

In cognitive science, empirical data collected from participants are the arbiters in model selection. Model discrimination thus depends on designing maximally informative experiments. It has been shown that adaptive design optimization (ADO) allows one to discriminate models as efficiently as possible in simulation experiments. In this paper we use ADO in a series of experiments with people to discriminate the Power, Exponential, and Hyperbolic models of memory retention, which has been a long-standing problem in cognitive science, providing an ideal setting in which to test the application of ADO for addressing questions about human cognition. Using an optimality criterion based on mutual information, ADO is able to find designs that are maximally likely to increase our certainty about the true model upon observation of the experiment outcomes. Results demonstrate the usefulness of ADO and also reveal some challenges in its implementation.