Abstract: Noted Optimal Design Theorist C S Cheng and his research collaborator M H Kao investigated the scope of study of optimal experimental designs in the context of fMRI studies.  We intend to review some aspects of this problem and, that too, from a small sample perspective.  An experimental subject [patient] is presented with a mental stimulus [e.g. picture] for a certain duration of time. During this presentation, the patient absorbs a sequence of mental stimuli along with a provision for intermediate ‘resting periods’ as well. The measurement refers to the ‘output’ in a well-specified reference ‘brain voxel’ and the purpose is to examine the response profiles to understand the nature and extent of local brain activity in response to the stimuli.
A linear model is envisaged and its purpose is to explain the mean response in terms of a constant [unknown parametric effect] and, additionally, a set of what are referred to as ‘h-parameters’. The h-parameters are also unknown. The inference problems center around h-parameters. Usual optimality considerations [such as A- and D-optimality] apply.
In this presentation the linear model will be presented, estimation issues will be discussed and related concepts such as ‘orthogonality’ and ‘balance’ will be elaborated.