Project Summary This proposal will deliver an innovative integrated statistical approach to analyze functional Magnetic Resonance Imaging (fMRI) data. The massive size of fMRI data has dictated, to date, a two-stage analysis, first reducing the temporal data at each voxel to a single activation value, followed by a spatial analysis for activated regions. Our basic premise is that an integrated one-stage, whole-brain data strategy will improve estimation and power even in studies with small sample sizes. The proposed methods will be generally applicable to fMRI data, but to illustrate the value of the methods, we will reanalyze publicly available datasets from two areas of importance to mental health. Suicide is a major public health concern, with the CDC reporting it to be the cause of two-thirds of all homicides in 2017, yet it remains highly unpredictable. Recent work provided fMRI data on 34 subjects upon exposing them to 10 words each with positive, negative or death-related connotations. Analysis of such involuntary data can reveal differences between suicide attempters and ideators, pinpoint subjects with elevated suicide risk, or identify the words with highest discriminatory power between groups, all useful outcomes for diagnosing and preventing suicide. Major Depressive Disorder (MDD) is projected to be the most prevalent cause of disease worldwide by 2030, yet only half of MDD patients receive treatment. A recent study provided fMRI data on 39 subjects using a validated emotional musical and nonmusical auditory paradigm. The long-term goal is to leverage music as a diagnostic or therapy for MDD. We will use our methods to re-evaluate sex, age, and other measured covariates, such as subject ratings of the music, which were previously only analyzed descriptively, to better detect differences in cerebral activation between MDD and controls, including one MDD subject with missing data due to excess motion in the machine. Our approach will directly model the complex, high-dimensional structure of fMRI data, including three spatial dimensions, time, and subject, by extending multivariate linear regression to a more natural and correct tensor-on-tensor linear regression framework, previously assumed to be computationally intractable. Our work will make it feasible and if the power advantages are as substantial as we expect, our approach should become the standard for fMRI data analysis in the future. The linear regression framework is familiar to practictioners, which along with the efficient, user-friendly software we will develop, will facilitate its wide adoption in the fMRI community. We develop tensor-on-tensor time series regression in Aim 1 and associated methods to classify patients and identify biomarkers in Aim 2. Application of our methods to a suicide and MDD datasets will serve to demonstrate the methods, while revealing actionable information about these two very important mental health challenges. More broadly, increased reliab...