Correcting the Bias of Spike Field Coherence Estimators Due to a Finite Number of Spikes

Grasse DW, Moxon KA. Correcting the bias of spike field coherence estimators due to a finite number of spikes. J Neurophysiol 104: 548-558, 2010. First published May 19, 2010; doi:10.1152/jn.00610.2009. The coherence between oscillatory activity in local field potentials (LFPs) and single neuron action potentials, or spikes, has been suggested as a neural substrate for the representation of information. The power spectrum of a spike-triggered average (STA) is commonly used to estimate spike field coherence (SFC). However, when a finite number of spikes is used to construct the STA, the coherence estimator is biased. We introduce here a correction for the bias imposed by the limited number of spikes available in experimental conditions. In addition, we present an alternative method for estimating SFC from an STA by using a filter bank approach. This method is shown to be more appropriate in some analyses, such as comparing coherence across frequency bands. The proposed bias correction is a linear transformation derived from an idealized model of spike-field interaction but is shown to hold in more realistic settings. Uncorrected and corrected SFC estimates from both estimation methods are compared across multiple simulated spike-field models and experimentally collected data. The bias correction was shown to reduce the bias of the estimators, but add variance. However, the corrected estimates had a reduced or unchanged mean squared error in the majority of conditions evaluated. The bias correction provides an effective way to reduce bias in an SFC estimator without increasing the mean squared error.