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Statistical analysis and modeling of neural data Lecture 7

Statistical analysis and modeling of neural data Lecture 7. Bijan Pesaran 26 Sept, 2007. Goals. Recap – spectral analysis for point processes. Coherency/Partial coherency as linear measures of association. Time-rescaling theorem and model validation. Spectral analysis for point processes.

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Statistical analysis and modeling of neural data Lecture 7

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  1. Statistical analysis and modeling of neural dataLecture 7 Bijan Pesaran 26 Sept, 2007

  2. Goals • Recap – spectral analysis for point processes. • Coherency/Partial coherency as linear measures of association. • Time-rescaling theorem and model validation

  3. Spectral analysis for point processes • Regression for temporal sequences • Naturally leads to measures of correlation • Statistical properties of estimators well-behaved

  4. Cross-spectral density

  5. Spectral quantities

  6. Coherence as linear association

  7. Substitute into loss: Minimize wrt B(f): Minimum value is: Where:

  8. Time lags in coherency

  9. Partial coherence

  10. Time-rescaling theorem Poisson with rate 1 History-dependent time rescaling

  11. Kolmogorov-Smirnov Test Empirical distribution function Critical values of the Kolmogorov-Smirnov Distribution

  12. Kolmogorov-Smirnov Test • Test for deviation from uniform distribution • Construct cumulative distribution function • Rank vs (95% confidence) (99% confidence)

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