Medidas de covariância direcionada e aplicações em neurociência
Resumo: We propose a causal wavelet decomposition of the covariance structure for bivariate locally stationary processes: the Directed Wavelet Covariance (DWC). Compared to Fourier-based quantities, wavelet-based estimators are more appropriate for non-stationary processes and processes with local patterns, outliers and rapid regime changes like in EEG experiments with the introduction of stimuli. Next we propose a decomposition for the variance of multivariate processes with more than two components: the Partial Directed Wavelet Covariance (pDWC). Considering a N-variate locally stationary process, the pDWC calculates the Directed Wavelet Covariance of X1(t) with X2(t) eliminating the effect of the other components X3(t), . . . , XN (t). The proposed Directed Wavelet Covariance decomposition is a different approach to deal with non-stationary processes in the context of causality. The use of wavelets is a gain and adds to the number of studies that can be addressed when Fourier transform does not apply. The pDWC is an alternative for multivariate processes and it removes linear influences from observed external components.
Local: Auditório do Instituto de Matemática e Estatística da UFBA