Constrained Multi-objective Designs for Functional MRI Experiments via A Modified NSGA-II

Functional magnetic resonance imaging (fMRI) is an advanced technology for studying brain functions. Due to the complexity and high cost of fMRI experiments, high quality multi-objective (MO) fMRI designs are in great demand; they help to render precise statistical inference, and are keys to the success of fMRI experiments. Here, we propose an efficient approach for obtaining MO fMRI designs. In contrast to existing methods, the proposed approach does not require users to specify weights for the different objectives, and can easily handle constraints to fulfill customized requirements.

TR Number: 
2010-07
Ming-Hung Kao, Abhyuday Mandal, and John Stufken
Key Words: 
Genetic algorithms, Hemodynamic response function, Multi-objective optimization, Design efficiency

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Assessment of Learning, For Learning, and As Learning in Statistics Education

J. Garfield and Franklin, C., Assessment of Learning, For Learning, and As Learning in Statistics Education, in Teaching Statistics in School Mathematics - Challenges for Teaching and Teacher Education: A Joint ICMI/IASE Study, vol. 14, Springer Publishers, 2011, pp. 133-145.

Monotone Convex Sequences and Cholesky Decomposition of Symmetric Toeplitz Matrices

This paper studies off-diagonal decay in symmetric Toeplitz matrices. It is shown that if the generating sequence of the matrix is monotone, positive and convex then the monitonicity and positivity are maintained through triangular decomposition. The work is motivated by recent results on explicit bounds for inverses of triangular matrices.

TR Number: 
2004-02
Kenneth S. Berenhaut and Dipankar Bandyopadhyay

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Robust Estimation of Mixture Complexity

Developing statistical procedures to determine the number of components, known as the mixture complexity, in finite mixture models remains an area of intense research. In many applications, it is important to find the mixture with fewest components that provides a satisfactory fit to the data. This article focuses on consistent estimation of unknown number of components in finite mixture models, when the exact form of the component densities are unknown but are postulated to be close to members of some parametric family.

TR Number: 
2004-03
Mi-Ja Woo and T.N. Sriram

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Pages

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