Bayesian estimation of evoked and induced responses

We describe an extension of our empirical Bayes approach to magnetoencephalography/electroencephalography (MEG/EEG) source reconstruction that covers both evoked and induced responses. The estimation scheme is based on classical covariance component estimation using restricted maximum likelihood (ReML). We have focused previously on the estimation of spatial covariance components under simple assumptions about the temporal correlations. Here we extend the scheme, using temporal basis functions to place constraints on the temporal form of the responses. We show how the same scheme can estimate evoked responses that are phase-locked to the stimulus and induced responses that are not. For a single trial the model is exactly the same. In the context of multiple trials, however, the inherent distinction between evoked and induced responses calls for different treatments of the underlying hierarchical multitrial model. We derive the respective models and show how they can be estimated efficiently using ReML. This enables the Bayesian estimation of evoked and induced changes in power or, more generally, the energy of wavelet coefficients.