The goal of this paper is to build a detector of event-related potentials (ERP) in single-trial EEG data. This problem can be reformulated as a parameter estimation problem, where the parameter of interest is the time of occurrence of the ERP. This type of detector has clinical applications (study of schizophrenia, fatigue), or applications in brain-computer-interfaces. However, the poor signal-to-noise ratio (SNR) and lack of understanding of the noise generating process make this a challenging task. In this paper, we take a Bayesian approach, samples are drawn from the posterior of the parameter of interest using Markov chain Monte Carlo (MCMC). Different noise covariances from Gaussian processes are tested. We show that it is possible to pick up the ERP signal in spite of the poor SNR with an appropriate choice of noise covariance structure.

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