Modeling Spectral Properties in Stationary Processes of Varying Dimensions with Applications to Brain Local Field Potential Signals.

In some applications, it is important to compare the stochastic properties of two multivariate time series that have unequal dimensions. A new method is proposed to compare the spread of spectral information in two multivariate stationary processes with different dimensions. To measure discrepancies, a frequency specific spectral ratio (FS-ratio) statistic is proposed and its asymptotic properties are derived. The FS-ratio is blind to the dimension of the stationary process and captures the proportion of spectral power in various frequency bands. Here we develop a technique to automatically identify frequency bands that carry significant spectral power. We apply our method to track changes in the complexity of a 32-channel local field potential (LFP) signal from a rat following an experimentally induced stroke. At every epoch (a distinct time segment from the duration of the experiment), the nonstationary LFP signal is decomposed into stationary and nonstationary latent sources and the complexity is analyzed through these latent stationary sources and their dimensions that can change across epochs. The analysis indicates that spectral information in the Beta frequency band (12-30 Hertz) demonstrated the greatest change in structure and complexity due to the stroke.

Reducing Brain Signal Noise in the Prediction of Economic Choices: A Case Study in Neuroeconomics.

In order to reduce the noise of brain signals, neuroeconomic experiments typically aggregate data from hundreds of trials collected from a few individuals. This contrasts with the principle of simple and controlled designs in experimental and behavioral economics. We use a frequency domain variant of the stationary subspace analysis (SSA) technique, denoted as DSSA, to filter out the noise (nonstationary sources) in EEG brain signals. The nonstationary sources in the brain signal are associated with variations in the mental state that are unrelated to the experimental task. DSSA is a powerful tool for reducing the number of trials needed from each participant in neuroeconomic experiments and also for improving the prediction performance of an economic choice task. For a single trial, when DSSA is used as a noise reduction technique, the prediction model in a food snack choice experiment has an increase in overall accuracy by around 10% and in sensitivity and specificity by around 20% and in AUC by around 30%, respectively.