A Bayesian methodology to estimate single-trial ERPs with application to the study of the P300 variability in cirrhosis

Several approaches, based on different assumptions and with various degree of theoretical sophistication and implementation complexity, have been developed for extracting the single-trial response of event related potentials (ERPs). In many of these methods, one of the major challenges is the exploitation of a priori knowledge. In this paper, we present a new method where the 2nd order statistical information on the background EEG and on the unknown ERP, necessary for the optimal filtering of each sweep in a Bayesian estimation framework, is, respectively, estimated from pre-stimulus data and obtained through a multiple integration of a white noise process model. The latter model is flexible and simple enough to be easily identifiable from the post-stimulus data thanks to a smoothing criterion. 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, a quantity determinable thanks to the employment of the Bayesian approach. Then, single-sweep estimation is dealt with within the same framework. The method is tested on simulated data and compared with a recently proposed estimation method based on radial-basis function (RBF) neural networks. Then, the method is also employed on real data with the aim of investigating the variability of the P300 component in cirrhotic vs normal subjects undertaken to a cognitive visual task.