The main focus of this paper is to find optimal experimental designs for functional magnetic resonance imaging (fMRI) experiments with compound stimuli by considering uncertain error correlations. We target designs, which are robust against a misspecification of error correlation. The maximin approach was proposed in the literature to tackle this problem. Unfortunately, obtaining maximin designs is computationally very expensive and time consuming. We propose to adapt Gaussian process (Kriging) that is widely used in spatial statistics and computer experiments to reduce the computational resource needed to find such designs. The proposed method is compared with a previously used approach. We observe that, in terms of the performance of the achieved designs, the results are quite similar between the two methods. In addition, our proposed Kriging approach requires less CPU time, and it is very efficient in obtaining good fMRI designs for compound stimuli experiments. The proposed approach is demonstrated via case studies.

Keywords : A-Optimality, fMRI, Genetic Algorithm, Kriging, Maximin Criterion.