A Bayesian method to estimate single-trial event-related potentials with application to the study of the P300 variability

We propose a Bayesian method to extract single-trial event related potentials (ERPs). The method is formulated in two stages. In the first stage, each of the N raw sweeps is processed by an individual “optimal” filter, where the 2nd order a priori statistical information on the background EEG and on the unknown ERP is, respectively, estimated from pre-stimulus data and obtained through the multiple integration of a white noise process model which is identifiable from post-stimulus data thanks to a smoothing criterion. Then, a mean ERP is determined as the weighted average of the filtered sweeps, where each weight is inversely proportional to the expected value of the norm of the correspondent filter error. In the second stage, single-sweep estimation is dealt with within the same framework, by using the average ERP estimated in the previous stage as a priori expected response. The method is successfully tested on simulated data and then employed on real data with the aim of investigating the variability of the P300 component during a cognitive visual task. A comparison with other literature methods is also performed. Results encourage further use of the proposed method to investigate if and how diseases, e.g., cirrhosis, are associated to differences in P300 variability.