Inference on Multi-level Partial Correlations based on Multi-subject Time Series Data

Partial correlations are commonly used to analyze the conditional dependence among variables. In this work, we propose a hierarchical model to study both the subject and population level partial correlations based on multi-subject time series data. Multiple testing procedures adaptive to temporally dependent data with false discovery proportion control are proposed to identify the nonzero partial correlations in both the subject and population levels. A computationally feasible algorithm is developed. Theoretical results and simulation studies demonstrate the good properties of the proposed procedures. We illustrate the application of the proposed methods in a real example of brain connectivity on fMRI data from normal healthy persons and patients with Parkinson’s disease.