The availability of powerful non-invasive neuroimaging techniques has given rise to various studies that aim to map the human brain. These studies focus on not only finding brain activation signatures but also on understanding the overall organization of functional communication in the brain network. Based on the principle that distinct brain regions are functionally connected and continuously share information with each other, various approaches to finding these functional networks have been proposed in the literature. In this paper, we present an overview of the most common methods to estimate and characterize functional connectivity in fMRI data. We illustrate these methodologies with resting-state functional MRI data from the Human Connectome Project, providing details of their implementation and insights on the interpretations of the results. We aim to guide researchers that are new to the field of neuroimaging by providing the necessary tools to estimate and characterize brain circuitry.

Medical imaging studies have collected high-dimensional imaging data to identify imaging biomarkers for diagnosis, screening, and prognosis, among many others. These imaging data are often represented in the form of a multi-dimensional array, called a tensor. The aim of this paper is to develop a tensor partition regression modeling (TPRM) framework to establish a relationship between low-dimensional clinical outcomes (e.g., diagnosis) and high-dimensional tensor covariates. Our TPRM is a hierarchical model and efficiently integrates four components: (i) a partition model, (ii) a canonical polyadic decomposition model, (iii) a principal components model, and (iv) a generalized linear model with a sparse inducing normal mixture prior. This framework not only reduces ultra-high dimensionality to a manageable level, resulting in efficient estimation, but also optimizes prediction accuracy in the search for informative sub-tensors. Posterior computation proceeds via an efficient Markov chain Monte Carlo algorithm. Simulation shows that TPRM outperforms several other competing methods. We apply TPRM to predict disease status (Alzheimer versus control) by using structural magnetic resonance imaging data obtained from the Alzheimer’s Disease Neuroimaging Initiative (ADNI) study.

We discuss hypothesis testing and compare different theories in light of observed or experimental data as fundamental endeavors in the sciences. Issues associated with the p-value approach and null hypothesis significance testing are reviewed, and the Bayesian alternative based on the Bayes factor is introduced, along with a review of computational methods and sensitivity related to prior distributions. We demonstrate how Bayesian testing can be practically implemented in several examples, such as the t-test, two-sample comparisons, linear mixed models, and Poisson mixed models by using existing software. Caveats and potential problems associated with Bayesian testing are also discussed. We aim to inform researchers in the many fields where Bayesian testing is not in common use of a well-developed alternative to null hypothesis significance testing and to demonstrate its standard implementation.

Predicting upcoming sensorimotor events means creating forward estimates of the body and the surrounding world. This ability is a fundamental aspect of skilled motor behavior and requires an accurate and constantly updated representation of the body and the environment. To test whether these prediction mechanisms could be affected by a peripheral injury, we employed an action observation and electroencephalogram (EEG) paradigm to assess the occurrence of prediction markers in anticipation of observed sensorimotor events in healthy and brachial plexus injury (BPI) participants. Nine healthy subjects and six BPI patients watched a series of video clips showing an actor’s hand and a colored ball in an egocentric perspective. The color of the ball indicated whether the hand would grasp it (hand movement), or the ball would roll toward the hand and touch it (ball movement), or no event would occur (no movement). In healthy participants, we expected to find distinct electroencephalographic activation patterns (EEG signatures) specific to the prediction of the occurrence of each of these situations. Cluster analysis from EEG signals recorded from electrodes placed over the sensorimotor cortex of control participants showed that predicting either an upcoming hand movement or the occurrence of a tactile event yielded specific neural signatures. In BPI participants, the EEG signals from the sensorimotor cortex contralateral to the dominant hand in the hand movement condition were different compared to the other conditions. Furthermore, there were no differences between ball movement and no movement conditions in the sensorimotor cortex contralateral to the dominant hand, suggesting that BPI blurred specifically the ability to predict upcoming tactile events for the dominant hand. These results highlight the role of the sensorimotor cortex in creating estimates of both actions and tactile interactions in the space around the body and suggest plastic effects on prediction coding following peripheral sensorimotor loss.

Task-evoked functional magnetic resonance imaging studies, such as the Human Connectome Project (HCP), are a powerful tool for exploring how brain activity is influenced by cognitive tasks like memory retention, decision-making, and language processing. A fast Bayesian function-on-scalar model is proposed for estimating population-level activation maps linked to the working memory task. The model is based on the canonical polyadic (CP) tensor decomposition of coefficient maps obtained for each subject. This decomposition effectively yields a tensor basis capable of extracting both common features and subject-specific features from the coefficient maps. These subject-specific features, in turn, are modeled as a function of covariates of interest using a Bayesian model that accounts for the correlation of the CP-extracted features. The dimensionality reduction achieved with the tensor basis allows for a fast MCMC estimation of population-level activation maps. This model is applied to one hundred unrelated subjects from the HCP dataset, yielding significant insights into brain signatures associated with working memory.

Task-evoked functional magnetic resonance imaging studies, such as the Human Connectome Project (HCP), are a powerful tool for exploring how brain activity is influenced by cognitive tasks like memory retention, decision-making, and language processing. A fast Bayesian function-on-scalar model is proposed for estimating population-level activation maps linked to the working memory task. The model is based on the canonical polyadic (CP) tensor decomposition of coefficient maps obtained for each subject. This decomposition effectively yields a tensor basis capable of extracting both common features and subject-specific features from the coefficient maps. These subject-specific features, in turn, are modeled as a function of covariates of interest using a Bayesian model that accounts for the correlation of the CP-extracted features. The dimensionality reduction achieved with the tensor basis allows for a fast MCMC estimation of population-level activation maps. This model is applied to one hundred unrelated subjects from the HCP dataset, yielding significant insights into brain signatures associated with working memory.