Conservative significance testing of tripartite statistical relations in multivariate neural data

An important goal in systems neuroscience is to understand the structure of neuronal interactions, frequently approached by studying functional relations between recorded neuronal signals. Commonly used pairwise measures (e.g., correlation coefficient) offer limited insight, neither addressing the specificity of estimated neuronal interactions nor potential synergistic coupling between neuronal signals. Tripartite measures, such as partial correlation, variance partitioning, and partial information decomposition, address these questions by disentangling functional relations into interpretable information atoms (unique, redundant, and synergistic). Here, we apply these tripartite measures to simulated neuronal recordings to investigate their sensitivity to noise. We find that the considered measures are mostly accurate and specific for signals with noiseless sources but experience significant bias for noisy sources.We show that permutation testing of such measures results in high false positive rates even for small noise fractions and large data sizes. We present a conservative null hypothesis for significance testing of tripartite measures, which significantly decreases false positive rate at a tolerable expense of increasing false negative rate. We hope our study raises awareness about the potential pitfalls of significance testing and of interpretation of functional relations, offering both conceptual and practical advice.