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{\bf Abstract}

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{\bf Methods for Addressing Spatial Correlations in Functional \\ Neuroimaging Data}

By

Gordana Derado
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Neuroimaging studies yield massive data sets that pose challenges for statistical analyses due, in part, to the intricate anatomical and functional properties of neurons. Our main objective is to uncover aspects of the complex spatial relationships present in functional neuroimaging data and to develop statistical methods that either evaluate or leverage those correlations. We propose the following methods to achieve our research goal: (i) a novel statistical approach to model the complex spatio-temporal structure of neuroimaging data, (ii) a method to evaluate the level of connectivity within functionally defined neural processing networks and (iii) a novel prediction framework for neuroimaging data based on a hierarchical Bayesian spatial model.

To date, there has been limited research on simultaneously modeling spatial correlations between the neural activity in distinct brain locations and temporal correlations between repeated neural activity measurements. We propose a spatio-temporal, autoregressive model which simultaneously accounts for spatial dependencies between voxels within the same anatomical region and for temporal dependencies between a subject's estimates from multiple sessions. We illustrate the application of our method using fMRI data from a cocaine addiction study.

Data-driven statistical approaches, such as ICA and cluster analysis, help to identify neural processing networks exhibiting similar patterns of activity. These approaches, however, do not quantify or statistically test the strength of the within-network relatedness between voxels. We adapt Moran's $I$ statistic for applicability to our neuroimaging analyses to measure the degree of functional autocorrelation within identified neural processing networks and to evaluate the statistical significance of the observed associations. We illustrate the use of our methodology with data from %two studies: 
an fMRI resting-state study of unipolar depression and a PET study of working memory among individuals with schizophrenia.

Recently there has been growing interest in the use of neuroimaging data as a tool for classification and prediction. We propose a novel Bayesian hierarchical framework for predicting follow-up neural activity based on the baseline functional neuroimaging data.
 %and relevant patient characteristics. 
The proposed model is multivariate and captures the correlations between brain activity at different scanning sessions. We illustrate the use of our proposed methodology with PET data from a study of Alzheimer's disease.

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%The model incorporates both short-range (between neighboring voxels) and long-range (between brain regions) correlations.
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%Spatial correlations are incorporated in the model in two ways: the short-range correlations between neighboring voxels are incorporated through a multivariate conditional autoregressive (CAR)  prior of the spatial parameters, while the long-range correlations between anatomical brain regions are incorporated through the covariance matrix of the random effect parameters. 