Experiment Design: Selection and Optimization
Session Chair: Pat Whitcomb, Stat-Ease, Inc.Multi-Objective fMRI Designs with Unequal Epoch Lengths via An Hybrid NSGA-II
Ming-Hung Kao
Arizona State University
Abstract: Functional magnetic resonance imaging (fMRI) is a pioneering technology for studying brain activity in response to mental stimuli. To render precise inference, a design sequence of stimuli that simultaneously achieves high statistical efficiencies and avoids psychological confounds is called for. In this work, we aim at obtaining such a multi-objective design. In contrast to previous studies, we allow different epoch lengths for different stimulus types. In addition, we adapt the non-dominated sorting genetic algorithm II (NSGA-II) to search for good designs, and incorporate knowledge about fMRI designs to improve the effectiveness of the search. We demonstrate that the proposed approach outperforms current methods in use. Moreover, we propose a new criterion for evaluating designs’ ability in circumventing psychological effects of anticipation and habituation. Rooted in the overlapping m-tuple test, the proposed criterion is sensitive to patterned design sequences and its value is easy to interpret.
Optimal Nonregular Designs of 32 runs and Their Projection Properties
Hong Zhou and Debra Ingram
Arkansas State University
Abstract: In this article, we study the projection properties of six inequivalent Hadamard matrices of order 32 using the generalized resolution criteria. In addition, we examine the practical use of the generalized aberration criteria in design selection and present the optimal designs with 32 runs and up to 10 factors which are embedded into those Hadamard matrices of order 32.
A Maximin Model-Robust Exchange Algorithm and its Generalization
Byran J. Smucker, Enrique del Castillo, and James L. Rosenberger
The Pennsylvania State University
We propose a model-robust exchange algorithm which produces exact experimental designs that maximize the minimum efficiency with respect to a set of user-specified models. The method relaxes the optimal design assumption that the model form is known completely in advance, and produces designs for which each possible model in the set will be well estimated. Further, we present a generalization of this method which allows the user to express varying levels of interest in each potential model; the resulting design will be suggestive of these differences. Some asymptotic properties of the maximin criterion are also explored, including a condition which guarantees a design with the same D-efficiencies for each possible model. The new algorithm provides experimenters with more control of these efficiencies than comparable procedures in the literature. We give examples to illustrate the procedure.
Quaternary-Code Designs: A New Class of Nonregular Fractional Factorial Designs
Frederick K. H. Phoa
Academia Sinica
Abstract: In the recent past, there was a realization that nonregular designs could be utilized in conducting ecient experiments with exibility, run size economy, and ability to exploit interactions. This led to a growing research on developing a general construction methodology of nonregular designs with good properties. Recent research indicates that designs constructed from quaternary codes (QC) are very promising. The talk provides a brief introduction on the methodology and supplementary techniques on how quaternary codes can be used from constructing designs. In addition, optimal 1=4th-, 1=8th- and 1=16th-fraction QC designs under maximum resolution, minimum aberration and maximum projectivity criteria are compared to the best regular designs of the same size. Finally, some ongoiing and future researches on QC designs are discussed.