This repository provides the codes for the paper "Inference on Multi-level Brain Connectivities based on fMRI Data" by Yumou Qiu and Xiao-Hua Zhou.

PC-individual.txt provides the function individual(X, ...) to estimate the locations of nonzero off-diagonal elements in a p by p partial correlation matrix, based on p-dimensional time series data X of size n. This function can be used to estimate the nonzero partial correlations among brain regions of an individual using the fMRI data.

The output cbind(recovery, Liu) is two p by p binary (0-1) matrices combining together by columns, where recovery is the output of the proposed method with 1 and 0 indicating significant nonzero and zero partial correlations respectively, and Liu is the output of the method for time independent data from the paper "Gaussian graphical model estimation with false discovery rate control" by Liu, W., The Annals of Statistics, 41, 2948–2978, 2013.

PC-population-1Sample.txt provides the function population(Z, ...) to estimate the population level partial correlation matrix based on p-dimensional time series data of size n from m individuals, where the input Z is a three-dimensional array of size n by p by m.

The output cbind(recovery, Liu, MinPv) is three p by p binary (0-1) matrices combining together by columns, with 1 and 0 indicating significant nonzero and zero population level partial correlations, respectively. Here, recovery is the output of the proposed method, and Liu and MinPv are the outputs from two existing multiple testing procedures based on subject level estimated partial correlations.

PC-population-2Sample.txt provides the function population2sample(Z1, Z2, ...) to test for the differences of population level partial correlation matrices from two groups. The input and output are similar to population(Z, ...) for the one-sample case.

The folder simulation provides the simualtion codes.