Bayesian analysis of phase data in EEG and MEG

Electroencephalography and magnetoencephalography recordings are non-invasive and temporally precise, making them invaluable tools in the investigation of neural responses in humans. However, these recordings are noisy, both because the neuronal electrodynamics involved produces a muffled signal and because the neuronal processes of interest compete with numerous other processes, from blinking to day-dreaming. One fruitful response to this noisiness has been to use stimuli with a specific frequency and to look for the signal of interest in the response at that frequency. Typically this signal involves measuring the coherence of response phase: here, a Bayesian approach to measuring phase coherence is described. This Bayesian approach is illustrated using two examples from neurolinguistics and its properties are explored using simulated data. We suggest that the Bayesian approach is more descriptive than traditional statistical approaches because it provides an explicit, interpretable generative model of how the data arises. It is also more data-efficient: it detects stimulus-related differences for smaller participant numbers than the standard approach.