Time Series Modelling for the Neurosciences: The Innovation Approach

Contemporary research in the neurosciences produces multivariate time series data from various modalities (EEG,MEG,FMRI,NIRS,etc.). In this talk a statistical framework for the analysis of various classes of such data by predictive modelling will be reviewed; in particular state space models will be discussed. Following a suggestion of Wiener, the residuals of the predictions are called "innovations". Parameter fitting and model comparison can be done by maximisation of likelihood, or preferably by minimisation of an information criterion, such as AIC or BIC. Applications to modelling FMRI and EEG time series will be presented; in the case of the EEG, a new approach to the inverse problem of estimating the source currents within brain will be discussed. Finally the topic of time series filtering and decomposition will be addressed, and an alternative to standard methods like Factor Analysis and Independent Component Analysis (ICA) will be presented.