In these notes we show a simplified expression for the Pairwise Phase Consistency (PPC) measure of Vinck et al. (2010). We illustrate it's relation to a bias-corrected spike-field coherence measure from Grasse et al. (2010), and discuss an third notion of spike-field coherence that is intermediate between the two.
Here, we use the term "event-triggered" rather than "spike-triggered", because we want to apply these measures to neural events other than spikes (e.g. beta-frequency transients in motor cortex).
Pairwise Phase Consistency
Vinck et al. (2010) define Pairwise Phase Consistency (PPC) as the expected dot product between all pairs of (spike-triggered) phase measurements.
\[\hat\Upsilon = \frac 2 {N(N-1)} \sum_{j=1..N-1} \sum_{k=j+1..N} \cos(\theta_j - \theta_k)\]
There is an alternative way to express PPC that is faster to calculate, and also reveals a relationship between PPC and similar alternatives.
