Effects of spike sorting error on the Granger causality index

Accurately sorting individual neurons is a technical challenge and plays an important role in identifying information flow among neurons. Spike sorting errors are almost unavoidable and can roughly be divided into two types: false positives (FPs) and false negatives (FNs). This study investigates how FPs and FNs affect results of the Granger causality (GC) analysis, a powerful method for detecting causal interactions between time series signals. We derived an explicit formula based on a first order vector autoregressive model to analytically study the effects of FPs and FNs. The proposed formula was able to reveal the intrinsic properties of the GC, and was verified by simulation studies. The effects of FPs and FNs were further evaluated using real experimental data from the ventroposterior medial nucleus of the thalamus. Some practical suggestions for spike sorting are also provided in this paper.