First Advisor
Shafie, Khalil
Document Type
Dissertation
Date Created
8-2021
Department
College of Education and Behavioral Sciences, Applied Statistics and Research Methods, ASRM Student Work
Abstract
Due to the functional nature of fMRI data, random field theory is used as a remedy to the multiple comparisons problem in brain signal detection. Traditionally, a Gaussian random field model is fitted to the functional data using this approach. However, fMRI data are not homogeneous, and there exist multiple underlying classes in functional data, so traditional inferential methods may fail. Here, we proposed a new model for signal detection in fMRI data in which we addressed the heterogeneity in such data. The proposed model is a mixture of two Gaussian random fields. We developed a Bayesian approach for hypothesis testing by using the notion of Bayes factor in infinite-dimensional parameter spaces. For such spaces, the Bayes factor is defined based on the concept of the Radon-Nikodym derivative. In our model, the Bayes factor is interpreted as the inverse of the expected value of a likelihood ratio with respect to the prior density of the model parameters. Obtaining the Bayes factor in infinite-dimensional parameter spaces is not analytically tractable, and we needed to compute it through numerical methods. Our methodology is empirically justified by Monte Carlo simulations and illustrated by an analysis of the simulated dataset.
Extent
113 pages
Rights Statement
Copyright is held by the author.
Recommended Citation
Forghaniarani, Mozhdeh, "BAYESIAN APPROACH TO THE MIXTURE OF GAUSSIAN RANDOM FIELDS AND ITS APPLICATION TO AN FUNCTIONAL MAGNETIC RESONANCE IMAGING STUDY" (2021). Dissertations. 825.
https://digscholarship.unco.edu/dissertations/825