Bayesian Approach to the Mixture of Gaussian Random Fields and Its Application to an fMRI Study

• Activity Number: 111 - Application and Development of Statistical Methods for Spatio-Temporal Data
• Type: Contributed
• Date/Time: Monday, August 8, 2022 : 8:30 AM to 10:20 AM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Mozhdeh Forghaniarani* and Khalil Shafie
• Companies: James Madison University and University of Northern Colorado
• Keywords: Random Field; Mixture Model; Bayes Factor; Radon-Nikodym derivative; infinite-dimensional parameter spaces

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. 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.