Moon- Ringo Ho

A Bayesian approach to modeling dynamic effective connectivity with fMRI data.

A state-space modeling approach for examining dynamic relationship between multiple brain regions was proposed in Ho, Ombao and Shumway (Ho, M.R., Ombao, H., Shumway, R., 2005. A State-Space Approach to Modelling Brain Dynamics to Appear in Statistica Sinica). Their approach assumed that the quantity representing the influence of one neuronal system over another, or effective connectivity, is time-invariant. However, more and more empirical evidence suggests that the connectivity between brain areas may be dynamic which calls for temporal modeling of effective connectivity. A Bayesian approach is proposed to solve this problem in this paper. Our approach first decomposes the observed time series into measurement error and the BOLD (blood oxygenation level-dependent) signals. To capture the complexities of the dynamic processes in the brain, region-specific activations are subsequently modeled, as a linear function of the BOLD signals history at other brain regions. The coefficients in these linear functions represent effective connectivity between the regions under consideration. They are further assumed to follow a random walk process so to characterize the dynamic nature of brain connectivity. We also consider the temporal dependence that may be present in the measurement errors. ML-II method (Berger, J.O., 1985. Statistical Decision Theory and Bayesian Analysis (2nd ed.). Springer, New York) was employed to estimate the hyperparameters in the model and Bayes factor was used to compare among competing models. Statistical inference of the effective connectivity coefficients was based on their posterior distributions and the corresponding Bayesian credible regions (Carlin, B.P., Louis, T.A., 2000. Bayes and Empirical Bayes Methods for Data Analysis (2nd ed.). Chapman and Hall, Boca Raton). The proposed method was applied to a functional magnetic resonance imaging data set and results support the theory of attentional control network and demonstrate that this network is dynamic in nature.

Time-dependent frequency domain principal components analysis of multichannel non-stationary signals

High dimensional multi-channel signals often exhibit multi-collinearities. This suggests that such signals can be decomposed into uncorrelated principal components with possibly lower dimension than that of the original signal. A time-localized frequency domain principal components analysis method is proposed for signals that exhibit locally stationary behavior. The first step is to form a mean square consistent estimate of the time-varying spectrum matrix by smoothing the time-localized periodograms using a kernel defined on the frequency axis whose span is selected automatically using a generalized cross-validation procedure that is based on the asymptotic gamma distribution. The eigenvalues of the spectral density estimate are then computed which are the estimated spectra of the principal components. In addition, one may apply a formal statistical procedure for testing whether the weights (components of an eigenvector) at a particular channel change over time. The proposed method can be easily implemented because it only requires the fast Fourier transform (FFT) and eigenvalue-eigenvector decomposition routines. An illustration is presented using a multi-channel brain waves data set recorded during an epileptic seizure.