Functional Magnetic Resonance Imaging is a relatively newly developed technique used to study neural activity in the human brain. This dissertation concerns advances in modeling and inference of neuroimaging data and consists of three projects: (1) nonparametric methods for combining different types of image-based test statistics; (2) parametric cluster mass inference via random field theory (RFT); and (3) optimizing the kernel size of the smoothed variance t-test.

Neuroimaging inferences are generally based on one of two statistics: cluster extent, the number of voxels within a cluster; and voxel intensity, the maximum voxel intensity in a cluster. In order to leverage the strength from both statistics, some combining methods have been proposed. Cluster mass is defined as the integral of suprathreshold intensities within a cluster. The nonparametric cluster mass inference method is considered a more sensitive method than the partial inference methods. Since the cluster mass statistic naturally combines the information from cluster extent and voxel intensity, and it is the product of cluster extent and suprathreshold average intensity within a cluster, we propose two combining functions using these two statistics within the permutation framework. We also develop a cluster mass inference method based on RFT.

It is shown that, for small group studies with 20 or fewer subjects, the smoothed variance t-test increases detection sensitivity and is a powerful alternative to the usual t-test. The reason is that the effective degrees of freedom (EDF) of a variance image will increase if the variance image is smoothed. However, the smoothing procedure induces bias. Although the EDF will increase with increasing smoothing kernel size, an increase in false positive regions may result as well. The purpose of the third part is to increase EDF in order to increase detection sensitivity while avoiding too much bias. In this work, we study the relationship between smoothing, the EDF, mean square error and bias.