[Mne_analysis] Goodness of fit statistic for TF-MxNE solution?

[Per Arnold Lysne]

Hello,



Does anyone know how to judge the goodness of fit of an MEG localization, in particular with regard to TF-MxNE? RMSE between the measured sensor data and that predicted by the localization seems to be a popular choice, but has limited value except in direct comparisons, and no test statistic.



I am tempted to use Wilk's Lambda, defined as Det(SS_error)/Det(SS_total), where SS_error and SS_total are the SSCP matrices as defined in a multivariate regression. In this case the data would be the array M of the sensor observations (#sensors x #samples), which is modeled by the G*Z*Phi-Hermetian term. Rao's-F then provides an approximate p-value. Unfortunately neither SS_error nor SS_total are full rank on my data and thus the determinants are not available. Additionally, I am struggling with the validity of this on a nonstationary system. (Ranks are both ~30, in SSCP matrices of 306x306, corresponding to a Neuromag scanner).



Thanks again,



Per Lysne, University of New Mexico



PS: Alex, which regard to your previous concern about using the TF-MxNE output with Granger analysis, I am using the nonparametric technique of Dhamala, Rangarajan and Ding (2008), which I believe avoids this problem: <http://www.sciencedirect.com/science/article/pii/S1053811908001328> http://www.sciencedirect.com/science/article/pii/S1053811908001328,<http://www.sciencedirect.com/science/article/pii/S1053811908001328> http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.100.018701

Phys. Rev. Lett. 100, 018701 (2008) - Estimating Granger Causality from Fourier and Wavelet Transforms of Time Series Data
Experiments in many fields of science and engineering yield data in the form of time series. The Fourier and wavelet transform-based nonparametric methods are used widely to study the spectral characteristics of these time series data. Here, we extend the framework of nonparametric spectral methods to include the estimation of Granger causality spectra for assessing directional influences. We illustrate the utility of the proposed methods using synthetic data from network models consisting of interacting dynamical systems.
Read more...<http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.100.018701>









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