Optimal experimental designs for fMRI when the model matrix is uncertain

This study concerns optimal designs for functional magnetic resonance imaging (fMRI) experiments when the model matrix of the statistical model depends on both the selected stimulus sequence (fMRI design), and the subject's uncertain feedback (e.g. answer) to each mental stimulus (e.g. question) presented to her/him. While practically important, this design issue is challenging. This mainly is because that the information matrix cannot be fully determined at the design stage, making it difficult to evaluate the quality of the selected designs. To tackle this challenging issue, we propose an easy-to-use optimality criterion for evaluating the quality of designs, and an efficient approach for obtaining designs optimizing this criterion. Compared with a previously proposed method, our approach requires a much less computing time to achieve designs with high statistical efficiencies.