In this research work, I propose Bayesian nonparametric approaches to model functional magnetic resonance imaging (fMRI) data. Due to the complex spatial and temporal correlation structure as well as the high dimensionality of fMRI data, statistical methods play a crucial role in the analysis of fMRI data. My research focuses on developing novel methods that incorporate both temporal and spatial correlations into a single modeling framework and simultaneously capture brain connectivity via appropriate priors.

First, I propose a spatio-temporal nonparametric Bayesian variable selection model of single-subject fMRI data. The method provides a joint analytical framework that allows to detect activated brain regions in response to a stimulus and infer the clustering of spatially remote voxels that exhibit fMRI time series with similar characteristics. I show good performance of the model on inference through simulations, and demonstrate via synthetic data analysis that the model outperforms methods implemented in the SPM8, a standard software for fMRI data analysis. I also apply the model to a fMRI study on attention to visual motion, and illustrate the results of activation detection and clustering.

Then I propose a Bayesian modeling approach to the analysis of multiple-subject fMRI data. The proposed method provides a unified, single stage, and probabilistically coherent Bayesian framework for the inference of task-related brain activity. Furthermore, I employ with advanced Bayesian nonparametric priors to tie the activation strengths within and across subjects, and graphical network priors to model the complex spatio-temporal correlation structure observed in fMRI scans from multiple subjects. I develop a variational Bayesian method for inference, in addition to a Markov Chain Monte Carlo (MCMC) method. I investigate the performance of the proposed model on simulated data, and compare its performance to competing methods on synthetic data. In an application to data from a fMRI study on breast cancer survivors, the model demonstrates the excellent estimation performance.