Estimating feedforward and feedback effective connections from fMRI time series: Assessments of statistical methods.

We test the adequacies of several proposed and two new statistical methods for recovering the causal structure of systems with feedback from synthetic BOLD time series. We compare an adaptation of the first correct method for recovering cyclic linear systems; Granger causal regression; a multivariate autoregressive model with a permutation test; the Group Iterative Multiple Model Estimation (GIMME) algorithm; the Ramsey et al. non-Gaussian methods; two non-Gaussian methods by Hyvärinen and Smith; a method due to Patel et al.

Unmixing for Causal Inference: Thoughts on McCaffrey and Danks.

McCaffrey and Danks have posed the challenge of discovering causal relations in data drawn from a mixture of distributions as an impossibility result in functional magnetic resonance (fMRI). We give an algorithm that addresses this problem for the distributions commonly assumed in fMRI studies and find that in testing, it can accurately separate data from mixed distributions. As with other obstacles to automated search, the problem of mixed distributions is not an impossible one, but rather a challenge.