Title: Correcting the Bias of Spike Field Coherence Estimators Due to a Finite Number of Spikes 1 2

25 The coherence between oscillatory activity in local field potentials (LFP) and single neuron action 26 potentials, or spikes, has been suggested as a neural substrate for the representation of information. 27 The power spectrum of a spike triggered average (STA) is commonly used to estimate spike field 28 coherence (SFC). However, when a finite number of spikes are used to construct the STA, the coherence 29 estimator is biased. We introduce here a correction for the bias imposed by the limited number of 30 spikes available in experimental conditions. In addition, we present an alternative method for 31 estimating SFC from an STA by using a filter bank approach. This method is shown to be more 32 appropriate in some analyses, such as comparing coherence across frequency bands. The proposed bias 33 correction is a linear transformation derived from an idealized model of spike-field interaction but is 34 shown to hold in more realistic settings. Uncorrected and corrected SFC estimates from both estimation 35 methods are compared across multiple simulated spike-field models and experimentally collected data. 36 The bias correction was shown to reduce the bias of the estimators, but add variance. However, the 37 corrected estimates had a reduced or unchanged mean squared error in the majority of conditions 38 evaluated. The bias correction provides an effective way to reduce bias in an SFC estimator without 39 increasing the mean squared error. 40 41