Advisor
Shafie, Khalil
Committee Member
Schaffer, Jay Ryan, 1969-
Committee Member
Lalonde, Trent L.
Department
Applied Statistics and Research Methods
Institution
University of Northern Colorado
Type of Resources
Text
Place of Publication
Greeley (Colo.)
Publisher
University of Northern Colorado
Date Created
5-1-2015
Genre
Thesis
Extent
133 pages
Digital Origin
Born digital
Description
Gaussian random field theory has been used extensively for correcting the multiple comparisons problem in neuroimaging over the past few decades. Traditionally the global maximum Xmax of the field is used as the test statistic for thresholding, and it was proved to be the likelihood ratio test statistic when testing one signal in a Gaussian scale space random field. Nonetheless, it is not uncommon to test for more than one signal in practice. Hence, the primary purpose of the current study was to propose a new likelihood ratio test statistic Ymax for testing two signals simultaneously in fMRI images based on Gaussian random field theory. Monte Carlo simulation was used to approximate the probability of Ymax through the empirical distribution in two-dimensional images and its power was also assessed under different conditions, varying the levels of distance, amplitude, and scale of the signals. This study also sought to explore the result in scale space where the width of smoothing kernel was added as an extra dimension. Critical values were successfully obtained for Ymax using simulation. In scale space, the thresholds were more stringent than the ones with fixed kernel width, but it also revealed that the power of scale space Ymax was higher. In both scale space and fixed smoothing width, distance, amplitude and scale of the signals all had effect on the power of Ymax to some extent. Nonetheless, Ymax did not seem to surpass the other conventional test statistics in terms of power. The reason could be the limited conditions being simulated in the present study. Further investigation is required to provide more information about the behavior of Ymax.
Notes
Dean's Citation for Excellence
Degree type
PhD
Degree Name
Doctoral
Language
English
Local Identifiers
Lu_unco_0161D_10390
Rights Statement
Copyright is held by author.
